{ "openapi": "3.1.0", "info": { "title": "CalculatorX Calculation API (Core Capabilities)", "version": "1.0.0", "description": "Deterministic calculation API for humans and AI agents. Computational verification is defined by CVP; Review-policy tiers (engine_tested / expert_verified) are supplemental. Prefer CVP Verified capabilities with CURRENT production attestation. Rate limits: REST POST /api/v1/calc/* ≈60/min/IP; MCP RPC ≈120/min; execute_calculation ≈30/min. Exceeded → 429 + Retry-After.", "contact": { "url": "https://www.calculatorx.com" } }, "servers": [ { "url": "https://www.calculatorx.com" } ], "tags": [ { "name": "Catalog" }, { "name": "CoreCapabilities", "description": "Core capability templates. Computational verification: CVP. Supplemental Review-policy tiers: candidate, engine_tested, internally_reviewed, expert_verified. Catalog token verified is L3 (expert_verified) only." }, { "name": "MCP", "description": "Remote MCP JSON-RPC at /mcp" } ], "paths": { "/api/v1/calc": { "get": { "operationId": "listCalculationEngines", "summary": "List calculation engines", "tags": [ "Catalog" ], "responses": { "200": { "description": "Engine catalog", "content": { "application/json": { "schema": { "type": "object" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } } } } }, "/mcp": { "get": { "operationId": "mcpDiscoverHttp", "summary": "MCP discovery (CalculatorX custom GET)", "tags": [ "MCP" ], "responses": { "200": { "description": "Server info and tool names", "content": { "application/json": { "schema": { "type": "object" } } } } } }, "post": { "operationId": "mcpJsonRpc", "summary": "MCP JSON-RPC (search / inspect / execute)", "description": "Dual-track: `2024-11-05` (optional initialize) and `2026-07-28` (require `Mcp-Method` / `Mcp-Name`). Tools: search_capabilities, inspect_capability, execute_calculation (free), compute_paid (Stage 0.5 opt-in, not live charging).", "tags": [ "MCP" ], "parameters": [ { "name": "MCP-Protocol-Version", "in": "header", "required": false, "schema": { "type": "string", "enum": [ "2026-07-28", "2024-11-05" ] }, "description": "Defaults to 2024-11-05 when omitted (legacy). Prefer 2026-07-28." }, { "name": "Mcp-Method", "in": "header", "required": false, "schema": { "type": "string" }, "description": "Required for 2026-07-28; must match JSON-RPC method" }, { "name": "Mcp-Name", "in": "header", "required": false, "schema": { "type": "string" }, "description": "Required for tools/call under 2026-07-28; must match params.name" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "additionalProperties": true } } } }, "responses": { "200": { "description": "JSON-RPC response", "content": { "application/json": { "schema": { "type": "object" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } } } } }, "/api/v1/units/convert": { "post": { "operationId": "convert_units", "summary": "UUCE unit conversion", "description": "Preview conversion between registered units with compatible quantity kinds and roles.", "parameters": [ { "in": "header", "name": "CalculatorX-Spec-Version", "schema": { "type": "string", "const": "0.1.1" } } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "additionalProperties": false, "properties": { "inputs": { "type": "object", "additionalProperties": false, "required": [ "value", "from_unit_id", "to_unit_id", "quantity_kind", "role", "snapshot" ], "properties": { "value": { "type": "string", "maxLength": 128, "pattern": "^([+-]?)(\\d+)(?:\\.(\\d+))?(?:[eE]([+-]?(?:[0-2]?\\d{1,2}|30[0-8])))?(?![\\s\\S])", "description": "Exact decimal text with up to three exponent digits and exponent magnitude at most 308." }, "from_unit_id": { "type": "string", "maxLength": 128, "pattern": "^cx:.+", "description": "Stable unit ID in the pinned registry." }, "to_unit_id": { "type": "string", "maxLength": 128, "pattern": "^cx:.+", "description": "Stable unit ID in the pinned registry." }, "quantity_kind": { "type": "string", "enum": [ "length", "mass", "duration", "temperature", "volume", "plane_angle", "solid_angle", "ratio", "area", "frequency", "angular_velocity", "speed", "acceleration", "force", "pressure", "energy", "torque", "power", "electric_current", "electric_potential", "electric_charge", "resistance", "capacitance", "inductance", "magnetic_flux", "magnetic_flux_density", "amount_of_substance", "luminous_intensity", "luminous_flux", "illuminance", "volume_flow_rate", "mass_flow_rate", "mass_density", "mass_concentration", "amount_concentration", "molar_mass", "dynamic_viscosity", "kinematic_viscosity", "surface_tension", "thermal_conductivity", "heat_transfer_coefficient", "thermal_resistance", "specific_heat_capacity", "heat_capacity", "specific_energy", "temperature_coefficient", "electrical_conductance", "electrical_resistivity", "electrical_conductivity", "apparent_power", "reactive_power", "area_moment", "section_modulus", "momentum", "areal_mass_density", "irradiance", "luminance", "radioactivity", "absorbed_dose", "dose_equivalent", "catalytic_activity", "information", "information_rate", "inverse_time", "voltage_temperature_coefficient", "transconductance_parameter", "resistance_per_length", "luminous_efficacy" ] }, "role": { "type": "string", "enum": [ "scalar", "point", "interval" ] }, "snapshot": { "const": "0.3.0-preview.3", "type": "string" } } }, "calculation_version": { "type": "string", "const": "0.1.1" }, "calculationVersion": { "type": "string", "const": "0.1.1" } } }, "example": { "inputs": { "value": "1", "from_unit_id": "cx:m", "to_unit_id": "cx:ft_i", "quantity_kind": "length", "role": "scalar", "snapshot": "0.3.0-preview.3" }, "calculation_version": "0.1.1" } } } }, "responses": { "200": { "description": "Exact expression, rounded decimal and binary64 representations, and snapshot bindings.", "content": { "application/json": { "schema": { "type": "object", "properties": { "status": { "const": "success" }, "capability_id": { "const": "units.convert" }, "tool_id": { "const": "convert-units" }, "calculation_version": { "const": "0.1.1" }, "availability": { "const": "preview" }, "verification": { "oneOf": [ { "type": "object", "properties": { "cvp": { "const": "not_assessed" }, "production_binding": { "const": "unbound" } }, "required": [ "cvp", "production_binding" ], "additionalProperties": false }, { "type": "object", "properties": { "cvp": { "const": "verified" }, "production_binding": { "const": "check_attestation" }, "calculation_version": { "const": "0.1.1" }, "execution_projection_sha256": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "evidence_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "verification_revision": { "type": "string" }, "manifest": { "type": "string" }, "attestation": { "type": "string" } }, "required": [ "cvp", "production_binding", "calculation_version", "execution_projection_sha256", "evidence_digest", "verification_revision", "manifest", "attestation" ], "additionalProperties": false } ] }, "result": { "type": "object", "properties": { "exact": { "type": "object", "properties": { "numerator": { "type": "string", "pattern": "^-?[0-9]+$" }, "denominator": { "type": "string", "pattern": "^[1-9][0-9]*$" }, "pi_power": { "type": "integer" } }, "required": [ "numerator", "denominator", "pi_power" ], "additionalProperties": false }, "decimal": { "type": "string", "description": "Decimal approximation to 34 significant digits, nearest ties to even." }, "binary64": { "type": [ "number", "null" ] }, "binary64_status": { "enum": [ "finite", "overflow", "underflow" ] }, "numerical_policy": { "const": "uuce-rational-pi-decimal34-v1" }, "rounding": { "type": "object", "properties": { "decimal_significant_digits": { "const": 34 }, "mode": { "const": "nearest_ties_to_even" }, "pi_approximation": { "type": "boolean" } }, "required": [ "decimal_significant_digits", "mode", "pi_approximation" ], "additionalProperties": false }, "input": { "type": "object", "properties": { "value": { "type": "string", "maxLength": 128, "pattern": "^([+-]?)(\\d+)(?:\\.(\\d+))?(?:[eE]([+-]?(?:[0-2]?\\d{1,2}|30[0-8])))?(?![\\s\\S])", "description": "Exact decimal text with up to three exponent digits and exponent magnitude at most 308." }, "quantity_kind": { "type": "string", "enum": [ "length", "mass", "duration", "temperature", "volume", "plane_angle", "solid_angle", "ratio", "area", "frequency", "angular_velocity", "speed", "acceleration", "force", "pressure", "energy", "torque", "power", "electric_current", "electric_potential", "electric_charge", "resistance", "capacitance", "inductance", "magnetic_flux", "magnetic_flux_density", "amount_of_substance", "luminous_intensity", "luminous_flux", "illuminance", "volume_flow_rate", "mass_flow_rate", "mass_density", "mass_concentration", "amount_concentration", "molar_mass", "dynamic_viscosity", "kinematic_viscosity", "surface_tension", "thermal_conductivity", "heat_transfer_coefficient", "thermal_resistance", "specific_heat_capacity", "heat_capacity", "specific_energy", "temperature_coefficient", "electrical_conductance", "electrical_resistivity", "electrical_conductivity", "apparent_power", "reactive_power", "area_moment", "section_modulus", "momentum", "areal_mass_density", "irradiance", "luminance", "radioactivity", "absorbed_dose", "dose_equivalent", "catalytic_activity", "information", "information_rate", "inverse_time", "voltage_temperature_coefficient", "transconductance_parameter", "resistance_per_length", "luminous_efficacy" ] }, "role": { "type": "string", "enum": [ "scalar", "point", "interval" ] } }, "required": [ "value", "quantity_kind", "role" ], "additionalProperties": false }, "from": { "type": "object", "properties": { "unit_id": { "type": "string" }, "revision": { "type": "string" }, "content_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "dependency_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" } }, "required": [ "unit_id", "revision", "content_digest", "dependency_digest" ], "additionalProperties": false }, "to": { "type": "object", "properties": { "unit_id": { "type": "string" }, "revision": { "type": "string" }, "content_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "dependency_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" } }, "required": [ "unit_id", "revision", "content_digest", "dependency_digest" ], "additionalProperties": false }, "snapshot": { "type": "object", "properties": { "version": { "const": "0.3.0-preview.3" }, "content_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "execution_projection_sha256": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "integrity_manifest_sha256": { "type": "string", "pattern": "^[a-f0-9]{64}$" } }, "required": [ "version", "content_digest", "execution_projection_sha256", "integrity_manifest_sha256" ], "additionalProperties": false } }, "required": [ "exact", "decimal", "binary64", "binary64_status", "numerical_policy", "rounding", "input", "from", "to", "snapshot" ], "additionalProperties": false, "if": { "properties": { "binary64_status": { "const": "finite" } } }, "then": { "properties": { "binary64": { "type": "number" } } }, "else": { "properties": { "binary64": { "type": "null" } } } }, "result_detail": { "type": "object", "properties": { "value": { "type": "object", "properties": { "exact": { "type": "object", "properties": { "numerator": { "type": "string", "pattern": "^-?[0-9]+$" }, "denominator": { "type": "string", "pattern": "^[1-9][0-9]*$" }, "pi_power": { "type": "integer" } }, "required": [ "numerator", "denominator", "pi_power" ], "additionalProperties": false }, "decimal": { "type": "string", "description": "Decimal approximation to 34 significant digits, nearest ties to even." }, "binary64": { "type": [ "number", "null" ] }, "binary64_status": { "enum": [ "finite", "overflow", "underflow" ] }, "numerical_policy": { "const": "uuce-rational-pi-decimal34-v1" }, "rounding": { "type": "object", "properties": { "decimal_significant_digits": { "const": 34 }, "mode": { "const": "nearest_ties_to_even" }, "pi_approximation": { "type": "boolean" } }, "required": [ "decimal_significant_digits", "mode", "pi_approximation" ], "additionalProperties": false }, "input": { "type": "object", "properties": { "value": { "type": "string", "maxLength": 128, "pattern": "^([+-]?)(\\d+)(?:\\.(\\d+))?(?:[eE]([+-]?(?:[0-2]?\\d{1,2}|30[0-8])))?(?![\\s\\S])", "description": "Exact decimal text with up to three exponent digits and exponent magnitude at most 308." }, "quantity_kind": { "type": "string", "enum": [ "length", "mass", "duration", "temperature", "volume", "plane_angle", "solid_angle", "ratio", "area", "frequency", "angular_velocity", "speed", "acceleration", "force", "pressure", "energy", "torque", "power", "electric_current", "electric_potential", "electric_charge", "resistance", "capacitance", "inductance", "magnetic_flux", "magnetic_flux_density", "amount_of_substance", "luminous_intensity", "luminous_flux", "illuminance", "volume_flow_rate", "mass_flow_rate", "mass_density", "mass_concentration", "amount_concentration", "molar_mass", "dynamic_viscosity", "kinematic_viscosity", "surface_tension", "thermal_conductivity", "heat_transfer_coefficient", "thermal_resistance", "specific_heat_capacity", "heat_capacity", "specific_energy", "temperature_coefficient", "electrical_conductance", "electrical_resistivity", "electrical_conductivity", "apparent_power", "reactive_power", "area_moment", "section_modulus", "momentum", "areal_mass_density", "irradiance", "luminance", "radioactivity", "absorbed_dose", "dose_equivalent", "catalytic_activity", "information", "information_rate", "inverse_time", "voltage_temperature_coefficient", "transconductance_parameter", "resistance_per_length", "luminous_efficacy" ] }, "role": { "type": "string", "enum": [ "scalar", "point", "interval" ] } }, "required": [ "value", "quantity_kind", "role" ], "additionalProperties": false }, "from": { "type": "object", "properties": { "unit_id": { "type": "string" }, "revision": { "type": "string" }, "content_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "dependency_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" } }, "required": [ "unit_id", "revision", "content_digest", "dependency_digest" ], "additionalProperties": false }, "to": { "type": "object", "properties": { "unit_id": { "type": "string" }, "revision": { "type": "string" }, "content_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "dependency_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" } }, "required": [ "unit_id", "revision", "content_digest", "dependency_digest" ], "additionalProperties": false }, "snapshot": { "type": "object", "properties": { "version": { "const": "0.3.0-preview.3" }, "content_digest": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "execution_projection_sha256": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "integrity_manifest_sha256": { "type": "string", "pattern": "^[a-f0-9]{64}$" } }, "required": [ "version", "content_digest", "execution_projection_sha256", "integrity_manifest_sha256" ], "additionalProperties": false } }, "required": [ "exact", "decimal", "binary64", "binary64_status", "numerical_policy", "rounding", "input", "from", "to", "snapshot" ], "additionalProperties": false, "if": { "properties": { "binary64_status": { "const": "finite" } } }, "then": { "properties": { "binary64": { "type": "number" } } }, "else": { "properties": { "binary64": { "type": "null" } } } }, "unit": { "type": "string" }, "formatted": { "type": "string" } }, "required": [ "value", "unit", "formatted" ], "additionalProperties": false } }, "required": [ "status", "capability_id", "tool_id", "calculation_version", "availability", "verification", "result", "result_detail" ], "additionalProperties": false } } } }, "400": { "description": "Invalid input, ambiguous unit, or incompatible quantity kind or role.", "content": { "application/json": { "schema": { "type": "object", "required": [ "status", "code" ], "properties": { "status": { "const": "error" }, "code": { "type": "string" }, "message": { "type": "string" }, "field": { "type": [ "string", "null" ] }, "http_status": { "type": "integer" }, "recoverable": { "type": "boolean" }, "capability_id": { "const": "units.convert" }, "calculation_version": { "const": "0.1.1" }, "candidates": { "type": "array", "items": { "type": "string" } }, "supported_snapshot": { "type": "string" }, "published_version": { "type": "string" } } } } } }, "405": { "description": "Method not allowed.", "content": { "application/json": { "schema": { "type": "object", "required": [ "status", "code" ], "properties": { "status": { "const": "error" }, "code": { "type": "string" }, "message": { "type": "string" }, "field": { "type": [ "string", "null" ] }, "http_status": { "type": "integer" }, "recoverable": { "type": "boolean" }, "capability_id": { "const": "units.convert" }, "calculation_version": { "const": "0.1.1" }, "candidates": { "type": "array", "items": { "type": "string" } }, "supported_snapshot": { "type": "string" }, "published_version": { "type": "string" } } } } } }, "409": { "description": "Calculation version or registry snapshot mismatch.", "content": { "application/json": { "schema": { "type": "object", "required": [ "status", "code" ], "properties": { "status": { "const": "error" }, "code": { "type": "string" }, "message": { "type": "string" }, "field": { "type": [ "string", "null" ] }, "http_status": { "type": "integer" }, "recoverable": { "type": "boolean" }, "capability_id": { "const": "units.convert" }, "calculation_version": { "const": "0.1.1" }, "candidates": { "type": "array", "items": { "type": "string" } }, "supported_snapshot": { "type": "string" }, "published_version": { "type": "string" } } } } } }, "413": { "description": "Request exceeds the Preview body limit.", "content": { "application/json": { "schema": { "type": "object", "required": [ "status", "code" ], "properties": { "status": { "const": "error" }, "code": { "type": "string" }, "message": { "type": "string" }, "field": { "type": [ "string", "null" ] }, "http_status": { "type": "integer" }, "recoverable": { "type": "boolean" }, "capability_id": { "const": "units.convert" }, "calculation_version": { "const": "0.1.1" }, "candidates": { "type": "array", "items": { "type": "string" } }, "supported_snapshot": { "type": "string" }, "published_version": { "type": "string" } } } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } } } } }, "/api/v1/cvp/receipt": { "get": { "operationId": "get_cvp_production_receipt", "summary": "Read a current production receipt for a capability version", "description": "The initial supported capability is units.convert. Check the returned binding against trusted release pins and use it before expires_at.", "parameters": [ { "in": "query", "name": "capability_id", "required": true, "schema": { "type": "string", "const": "units.convert" } }, { "in": "query", "name": "calculation_version", "required": true, "schema": { "type": "string", "const": "0.1.1" } } ], "responses": { "200": { "description": "Current production binding, probe time, expiry and audit links." }, "400": { "description": "Both query parameters are required." }, "404": { "description": "Unsupported capability or calculation version." }, "503": { "description": "A current receipt is unavailable on this origin." } } } }, "/api/v1/units/preflight": { "get": { "operationId": "get_unit_conversion_agent_policy", "summary": "Read the active UUCE preflight policy and allowed scope", "responses": { "200": { "description": "Policy version, supported unit pairs, required context and exact decimal limits." } } }, "post": { "operationId": "preflight_unit_conversion", "summary": "Check an automatic UUCE conversion against policy and production binding", "description": "Supply a policy and calculation version, conversion inputs and trusted release pins in trust. Request a new decision before each automatic use.", "externalDocs": { "url": "https://www.calculatorx.com/developers/units#agent-preflight" }, "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "policy_version", "calculation_version", "trust", "inputs" ], "additionalProperties": false, "properties": { "policy_version": { "type": "string" }, "calculation_version": { "type": "string" }, "trust": { "type": "object", "description": "Independently pinned values in the production receipt binding format." }, "context": { "type": "object", "properties": { "use_case": { "type": "string", "const": "standalone_low_risk" } } }, "inputs": { "type": "object", "additionalProperties": false, "required": [ "snapshot" ], "properties": { "value": { "type": "string", "maxLength": 128, "pattern": "^([+-]?)(\\d+)(?:\\.(\\d+))?(?:[eE]([+-]?(?:[0-2]?\\d{1,2}|30[0-8])))?(?![\\s\\S])", "description": "Exact decimal text with up to three exponent digits and exponent magnitude at most 308." }, "from_unit_id": { "type": "string", "maxLength": 128, "pattern": "^cx:.+", "description": "Stable unit ID in the pinned registry." }, "to_unit_id": { "type": "string", "maxLength": 128, "pattern": "^cx:.+", "description": "Stable unit ID in the pinned registry." }, "quantity_kind": { "type": "string", "enum": [ "length", "mass", "duration", "temperature", "volume", "plane_angle", "solid_angle", "ratio", "area", "frequency", "angular_velocity", "speed", "acceleration", "force", "pressure", "energy", "torque", "power", "electric_current", "electric_potential", "electric_charge", "resistance", "capacitance", "inductance", "magnetic_flux", "magnetic_flux_density", "amount_of_substance", "luminous_intensity", "luminous_flux", "illuminance", "volume_flow_rate", "mass_flow_rate", "mass_density", "mass_concentration", "amount_concentration", "molar_mass", "dynamic_viscosity", "kinematic_viscosity", "surface_tension", "thermal_conductivity", "heat_transfer_coefficient", "thermal_resistance", "specific_heat_capacity", "heat_capacity", "specific_energy", "temperature_coefficient", "electrical_conductance", "electrical_resistivity", "electrical_conductivity", "apparent_power", "reactive_power", "area_moment", "section_modulus", "momentum", "areal_mass_density", "irradiance", "luminance", "radioactivity", "absorbed_dose", "dose_equivalent", "catalytic_activity", "information", "information_rate", "inverse_time", "voltage_temperature_coefficient", "transconductance_parameter", "resistance_per_length", "luminous_efficacy" ] }, "role": { "type": "string", "enum": [ "scalar", "point", "interval" ] }, "snapshot": { "const": "0.3.0-preview.3", "type": "string" } } } } } } } }, "responses": { "200": { "description": "Policy decision. ALLOW includes the receipt and the approved execution request.", "content": { "application/json": { "schema": { "type": "object", "required": [ "contract", "policy_version", "decision", "code" ], "properties": { "decision": { "enum": [ "ALLOW", "DENY", "NEED_CONTEXT" ] } } } } } }, "400": { "description": "Invalid JSON." }, "413": { "description": "Request exceeds the preflight body limit." }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } } } } }, "/api/v1/calc/amps-to-va": { "post": { "operationId": "calculate_electrical_apparent_power", "summary": "Electrical apparent power", "description": "Single-phase or balanced sinusoidal three-phase (L-L) AC apparent power: amps↔VA and amps→kVA. (calculation_version 1.4.3)\n\nSemantic capability: `electrical.apparent_power`.\n\nCalculation version: `1.4.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not for DC systems\n\nLimitation: Not for unbalanced or nonsinusoidal three-phase; √3 formula assumes balanced sinusoidal V_LL = √3 V_LN and equal line currents\n\nLimitation: Not for line-to-neutral three-phase mode\n\nLimitation: Not for equipment protection or conductor sizing\n\nLimitation: When power_factor is supplied, REST/MCP include derived.estimated_real_power; omitted when λ is absent", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.3" ] }, "description": "Pin calculation_version (published: 1.4.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.apparent_power.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.3", "examples": [ "1.4.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.apparent_power.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ohms-law": { "post": { "operationId": "calculate_electrical_ohms_law", "summary": "Ohm's law", "description": "Solve any two of V, I, R, P for resistive DC / AC RMS circuits. (calculation_version 1.5.1)\n\nSemantic capability: `electrical.ohms_law`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Resistive model only\n\nLimitation: Not for reactive impedance networks\n\nLimitation: Fewer than two inputs → NEEDS_TWO_INPUTS; non-finite → INVALID_NUMBER\n\nLimitation: Zero divisors yield 0 for dependents (soft boundary)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.ohms_law.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.ohms_law.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/watts-to-amps": { "post": { "operationId": "calculate_electrical_watts_amps", "summary": "Watts ↔ amps", "description": "Convert real power and current for DC, single-phase, or three-phase with power factor. (calculation_version 1.4.1)\n\nSemantic capability: `electrical.watts_amps`.\n\nCalculation version: `1.4.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not for unbalanced three-phase\n\nLimitation: Not for line-to-neutral three-phase as a separate mode\n\nLimitation: Not a substitute for breaker or conductor sizing", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.1" ] }, "description": "Pin calculation_version (published: 1.4.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_amps.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.1", "examples": [ "1.4.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_amps.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/power-factor": { "post": { "operationId": "calculate_electrical_power_factor", "summary": "Power factor", "description": "Compute apparent power S, power factor λ, and reactive power Q from RMS V, I, and real power P for 1φ or balanced 3φ. (calculation_version 1.5.1)\n\nSemantic capability: `electrical.power_factor`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Correction capacitor estimate is UI-only (not part of the API result)\n\nLimitation: Not for harmonic-rich or engineered bank design\n\nLimitation: When P > S, PF is capped at 1 and Q = 0 (soft clamp)\n\nLimitation: Voltage must be > 0 (VOLTAGE_MUST_BE_POSITIVE); zero volts is not a valid S=0 shortcut", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.power_factor.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.power_factor.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/voltage-drop": { "post": { "operationId": "calculate_electrical_voltage_drop", "summary": "Voltage drop", "description": "Estimate conductor voltage drop from current, one-way length, and Ω/km for DC / resistive 1φ or balanced 3φ (resistance-only, PF≈1). Always returns conductor I²R loss P_loss. Optional V_system adds percent drop and estimated load voltage; optional u_* compose expanded uncertainty on V_drop via Uncertainty Engine. (calculation_version 1.5.2)\n\nSemantic capability: `electrical.voltage_drop`.\n\nCalculation version: `1.5.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Resistance-only estimate — AC reactance neglected; AC modes assume PF ≈ 1\n\nLimitation: Not a substitute for code-compliant cable sizing or ampacity\n\nLimitation: 3φ V_system is line-to-line; percent_drop and V_load use that same basis\n\nLimitation: Zero I/length/R → 0 V (valid); negatives → VALUE_MUST_BE_NON_NEGATIVE\n\nLimitation: mode must be dc or three (INVALID_MODE otherwise); REST/UI default dc if omitted\n\nLimitation: V_system if set must be > 0 (VALUE_MUST_BE_POSITIVE); omit it to return volts only\n\nLimitation: Optional u_* use GUM sensitivity only; empty u_* still returns { V_drop, R_one_way, P_loss, … } without uncertainty\n\nLimitation: Engine tested, source checked, evidence published (L1). Named expert review is a higher assurance tier (L3), not required for engine-tested status. Not a code-compliance certification.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.2" ] }, "description": "Pin calculation_version (published: 1.5.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.voltage_drop.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.2", "examples": [ "1.5.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.voltage_drop.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/voltage-divider": { "post": { "operationId": "calculate_electrical_voltage_divider", "summary": "Voltage divider", "description": "Solve unloaded two-resistor divider networks from exactly three of Vin, R1, R2, Vout; also returns series current, resistor power, divider ratio, and Thevenin output resistance Rth. (calculation_version 1.5.1)\n\nSemantic capability: `electrical.voltage_divider`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Unloaded two-resistor divider only\n\nLimitation: Canonical input is exactly three of Vin, R1, R2, Vout\n\nLimitation: Fewer than three inputs → NEEDS_THREE_INPUTS\n\nLimitation: All four inputs → TOO_MANY_INPUTS (not a consistency check)\n\nLimitation: Solving R1/R2 requires Vin > Vout > 0 (INVALID_DIVIDER_VOLTAGES otherwise)\n\nLimitation: R1+R2=0 when solving Vout → RESISTANCE_MUST_BE_POSITIVE\n\nLimitation: Not for loaded dividers, AC reactive dividers, or RF", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.voltage_divider.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.voltage_divider.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/energy-consumption": { "post": { "operationId": "calculate_electrical_energy_consumption", "summary": "Energy consumption", "description": "Convert watts and hours to kilowatt-hours. (calculation_version 1.4.2)\n\nSemantic capability: `electrical.energy_consumption`.\n\nCalculation version: `1.4.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Assumes constant power over the stated hours\n\nLimitation: W and hours must be ≥ 0 (VALUE_MUST_BE_NON_NEGATIVE)\n\nLimitation: UI daily month/year projections are presentation-only; engine returns period kWh", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.2" ] }, "description": "Pin calculation_version (published: 1.4.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.energy_consumption.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.2", "examples": [ "1.4.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.energy_consumption.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/energy-cost": { "post": { "operationId": "calculate_electrical_energy_cost", "summary": "Energy cost", "description": "Estimate electricity cost from watts/hours or kWh and a unit rate. (calculation_version 1.4.2)\n\nSemantic capability: `electrical.energy_cost`.\n\nCalculation version: `1.4.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Usage cost only — standing charge and tax not included\n\nLimitation: W, hours, days, kWh, and rate must be ≥ 0\n\nLimitation: Hours per day must be ≤ 24 (HOURS_PER_DAY_OUT_OF_RANGE)\n\nLimitation: Zero W/hours/days/kWh/rate → 0", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.2" ] }, "description": "Pin calculation_version (published: 1.4.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.energy_cost.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.2", "examples": [ "1.4.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.energy_cost.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ev-to-volts": { "post": { "operationId": "calculate_electrical_ev_voltage", "summary": "eV to Volts", "description": "Relate electronvolt energy to electric potential difference through E = qV using charge magnitude and the exact SI elementary charge. (calculation_version 1.3.0)\n\nSemantic capability: `electrical.ev_voltage`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Charge is magnitude only — electron (−e) vs proton (+e) sign is not modeled\n\nLimitation: Q = 0 when solving for voltage → ZERO_CHARGE (not 0 V)\n\nLimitation: Uses exact SI e = 1.602176634×10⁻¹⁹ C\n\nLimitation: Not a pure eV↔V unit conversion; ΔE = qΔV", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.ev_voltage.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.ev_voltage.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/volts-to-ev": { "post": { "operationId": "calculate_electrical_ev_voltage_alias_volts_to_ev", "summary": "eV to Volts (volts-to-ev page alias)", "description": "Relate electronvolt energy to electric potential difference through E = qV using charge magnitude and the exact SI elementary charge. (calculation_version 1.3.0)\n\nSemantic capability: `electrical.ev_voltage`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Charge is magnitude only — electron (−e) vs proton (+e) sign is not modeled\n\nLimitation: Q = 0 when solving for voltage → ZERO_CHARGE (not 0 V)\n\nLimitation: Uses exact SI e = 1.602176634×10⁻¹⁹ C\n\nLimitation: Not a pure eV↔V unit conversion; ΔE = qΔV", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.ev_voltage.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.ev_voltage.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/watt-volt-amp": { "post": { "operationId": "calculate_electrical_watt_volt_amp", "summary": "Watt / volt / amp", "description": "Solve any two of P, V, I, R for simple resistive power relationships. (calculation_version 1.5.1)\n\nSemantic capability: `electrical.watt_volt_amp`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Resistive model only\n\nLimitation: Fewer than two inputs throws; zero divisors yield 0 for dependents", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.watt_volt_amp.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.watt_volt_amp.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/power": { "post": { "operationId": "calculate_electrical_power", "summary": "Electric power", "description": "Real power in watts from V×I×PF (DC / 1φ / balanced 3φ L-L), from I²R, or average power E/Δt. PF=0 is valid (P=0); blank PF defaults to 1. Δt=0 is INVALID_TIME_INTERVAL. (calculation_version 1.3.0)\n\nSemantic capability: `electrical.power`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: V×I path is real power P, not apparent power S (use amps-to-va)\n\nLimitation: Three-phase is balanced sinusoidal L-L only\n\nLimitation: I²R tab is I+R only; V²/R is Ohm’s law, not a third tab\n\nLimitation: PF blank → 1; PF=0 → P=0; PF outside [0,1] → INVALID_POWER_FACTOR\n\nLimitation: Δt ≤ 0 → INVALID_TIME_INTERVAL (not a soft 0 W)\n\nLimitation: Sinusoidal PF teaching model; true PF with harmonics is not computed", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.power.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.power.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/electricity": { "post": { "operationId": "calculate_electrical_electricity_bill", "summary": "Electricity bill", "description": "Estimate a simple electricity bill from kWh or meter readings plus rates and fees. (calculation_version 1.3.1)\n\nSemantic capability: `electrical.electricity_bill`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not for TOU / slab tariffs / export credits\n\nLimitation: Current meter reading must be ≥ previous reading; otherwise METER_READING_DECREASED is returned\n\nLimitation: Fee is a lump sum only; percentage and per-kWh taxes are not calculated", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.electricity_bill.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.electricity_bill.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/amps-to-kw": { "post": { "operationId": "calculate_electrical_amps_to_kw", "summary": "Amps to kW", "description": "Convert current and voltage to real power in kW (or reverse) for DC, single-phase AC, and balanced three-phase L-L. (calculation_version 1.4.3)\n\nSemantic capability: `electrical.amps_to_kw`.\n\nCalculation version: `1.4.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: DC, single-phase AC, or balanced three-phase L-L only\n\nLimitation: DC payloads must omit power_factor\n\nLimitation: Not for unbalanced three-phase\n\nLimitation: Not for line-to-neutral three-phase as a selectable mode\n\nLimitation: AC power_factor must be in (0, 1] — no soft coerce\n\nLimitation: V ≤ 0 → VOLTAGE_MUST_BE_POSITIVE\n\nLimitation: factor is an implementation constant (0.001) and is not an Agent input", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.3" ] }, "description": "Pin calculation_version (published: 1.4.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.amps_to_kw.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.3", "examples": [ "1.4.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.amps_to_kw.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/amps-to-volts": { "post": { "operationId": "calculate_electrical_amps_to_volts", "summary": "Amps to volts", "description": "Solve voltage from current plus resistance or power, and reverse to current. Watts paths cover DC, AC single-phase, and balanced three-phase L-L. (calculation_version 1.4.2)\n\nSemantic capability: `electrical.amps_to_volts`.\n\nCalculation version: `1.4.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Composite page: ohms path is V=IR; watts path is P/(I·PF) with optional √3\n\nLimitation: Not for converting amps to volts from current alone\n\nLimitation: JSON Schema is a callable-input envelope (types/required/enums). Zeros, negatives, and PF outside (0,1] may be schema-valid; the engine returns stable error codes\n\nLimitation: DC payloads must omit power_factor. REST may still send PF on DC: ignored with POWER_FACTOR_IGNORED\n\nLimitation: AC watts paths require power_factor in (0, 1]. UI initializes AC PF to 1.0; Agent/API clients must send it. Explicit PF=0 is POWER_FACTOR_OUT_OF_RANGE, not a silent 1\n\nLimitation: P>0 with I=0 → CURRENT_MUST_BE_NONZERO; V≠0 with R=0 → RESISTANCE_MUST_BE_NONZERO; 0/0 → UNDEFINED\n\nLimitation: IEEE-754 binary64; non-finite results → NON_FINITE_RESULT\n\nLimitation: Not for unbalanced three-phase", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.2" ] }, "description": "Pin calculation_version (published: 1.4.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.amps_to_volts.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.2", "examples": [ "1.4.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.amps_to_volts.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kva-to-amps": { "post": { "operationId": "calculate_electrical_kva_to_amps", "summary": "kVA to amps", "description": "Convert apparent power in kVA to line current for single- or three-phase systems. (calculation_version 1.4.1)\n\nSemantic capability: `electrical.kva_to_amps`.\n\nCalculation version: `1.4.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not for unbalanced three-phase\n\nLimitation: Not for line-to-neutral as a separate UI mode\n\nLimitation: No power factor on apparent path\n\nLimitation: V>0 hard — VOLTAGE_MUST_BE_POSITIVE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.1" ] }, "description": "Pin calculation_version (published: 1.4.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.kva_to_amps.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.1", "examples": [ "1.4.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.kva_to_amps.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/va-to-kva": { "post": { "operationId": "calculate_electrical_va_to_kva", "summary": "VA to kVA", "description": "Scale volt-amperes to kilovolt-amperes (÷1000) or reverse (×1000). (calculation_version 1.3.1)\n\nSemantic capability: `electrical.va_to_kva`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not a watts/kW conversion — power factor is not used\n\nLimitation: Physical use assumes non-negative apparent power", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.va_to_kva.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.va_to_kva.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kva-to-kw": { "post": { "operationId": "calculate_electrical_kva_to_kw", "summary": "kVA to kW", "description": "Convert apparent power to real power using power factor: kW = kVA × PF. (calculation_version 1.4.1)\n\nSemantic capability: `electrical.kva_to_kw`.\n\nCalculation version: `1.4.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: PF ∈ (0,1] hard\n\nLimitation: No voltage/phase required", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.1" ] }, "description": "Pin calculation_version (published: 1.4.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.kva_to_kw.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.1", "examples": [ "1.4.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.kva_to_kw.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kw-to-va": { "post": { "operationId": "calculate_electrical_kw_to_va", "summary": "kW to VA", "description": "Estimate apparent power in VA from real power and power factor. (calculation_version 1.3.1)\n\nSemantic capability: `electrical.kw_to_va`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: PF ∈ (0,1] hard\n\nLimitation: Built-in kW↔VA scale ×1000", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.kw_to_va.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.kw_to_va.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/watts-to-va": { "post": { "operationId": "calculate_electrical_watts_to_va", "summary": "Watts to VA", "description": "Convert real power (W) and apparent power (VA) using power factor — PF required (electrical.active_power_from_apparent_power / apparent_from_P_pf). (calculation_version 1.3.1)\n\nSemantic capability: `electrical.watts_to_va`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not for voltage/current→VA (use amps-to-va)\n\nLimitation: PF must be in (0, 1] — PF=0 → POWER_FACTOR_OUT_OF_RANGE (not a soft zero)\n\nLimitation: Roadmap model op: real_from_S_pf / apparent_from_P_pf", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_va.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_va.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/watts-to-kva": { "post": { "operationId": "calculate_electrical_watts_to_kva", "summary": "Watts to kVA", "description": "Convert real power in watts to apparent power in kVA using power factor: kVA = W ÷ (1000 × PF). Same PF rule as Watts to VA, scaled to kilovolt-amperes. (calculation_version 1.3.1)\n\nSemantic capability: `electrical.watts_to_kva`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: PF ∈ (0,1] hard\n\nLimitation: No voltage/phase required\n\nLimitation: Shares the scale-quotient helper with kWh→W; contracts are distinct (PF vs time)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_kva.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_kva.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kwh-to-watts": { "post": { "operationId": "calculate_electrical_kwh_to_watts", "summary": "kWh to Watts", "description": "Convert energy in kWh and a time period into average power in watts: W = 1000 × kWh ÷ h. Reverse: kWh = W × h ÷ 1000. (calculation_version 1.2.1)\n\nSemantic capability: `electrical.kwh_to_watts`.\n\nCalculation version: `1.2.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Average power over the interval — not instantaneous peak\n\nLimitation: Time must be in hours\n\nLimitation: Shares the scale-quotient helper with W→kVA; contracts are distinct (time vs PF)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.1" ] }, "description": "Pin calculation_version (published: 1.2.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.kwh_to_watts.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.1", "examples": [ "1.2.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.kwh_to_watts.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kwh-to-kw": { "post": { "operationId": "calculate_electrical_kwh_to_kw", "summary": "kWh to kW", "description": "Convert energy in kWh and a time period into average power in kilowatts: kW = kWh ÷ h. Reverse: kWh = kW × h. (calculation_version 1.2.1)\n\nSemantic capability: `electrical.kwh_to_kw`.\n\nCalculation version: `1.2.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Average power over the interval — not instantaneous peak\n\nLimitation: Time must be in hours", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.1" ] }, "description": "Pin calculation_version (published: 1.2.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.kwh_to_kw.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.1", "examples": [ "1.2.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.kwh_to_kw.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/watts-to-volts": { "post": { "operationId": "calculate_electrical_watts_to_volts", "summary": "Watts to Volts", "description": "Find voltage from power and current, or from power and resistance. Reverse: watts from volts and current. (calculation_version 1.3.1)\n\nSemantic capability: `electrical.watts_to_volts`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: RMS quantities for AC\n\nLimitation: Balanced three-phase when phase is three\n\nLimitation: Ohms path is resistive magnitude, V = √(P·R)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_volts.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_volts.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/volts-to-joules": { "post": { "operationId": "calculate_electrical_volts_to_joules", "summary": "Volts to Joules", "description": "Relate voltage and charge to energy: E = V × Q (1 V = 1 J/C). Reverse: V = E ÷ Q. (calculation_version 1.2.0)\n\nSemantic capability: `electrical.volts_to_joules`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cannot convert volts to joules without a charge (or equivalent)\n\nLimitation: Shares the product helper with W→J; contracts are distinct (Q vs t)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.volts_to_joules.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.volts_to_joules.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/watts-to-joules": { "post": { "operationId": "calculate_electrical_watts_to_joules", "summary": "Watts to Joules", "description": "Convert power and time to energy: E(J) = P(W) × t(s). Reverse: P = E ÷ t. 1 W = 1 J/s. (calculation_version 1.2.1)\n\nSemantic capability: `electrical.watts_to_joules`.\n\nCalculation version: `1.2.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cannot convert watts to joules without a duration\n\nLimitation: Shares the product helper with V→J; contracts are distinct (t vs Q)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.1" ] }, "description": "Pin calculation_version (published: 1.2.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_joules.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.1", "examples": [ "1.2.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.watts_to_joules.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/volts-to-kw": { "post": { "operationId": "calculate_electrical_volts_to_kw", "summary": "Volts to kW", "description": "Estimate real power from voltage, current, phase, and power factor. (calculation_version 1.3.1)\n\nSemantic capability: `electrical.volts_to_kw`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: PF ∈ (0,1] hard — FRACTION_OUT_OF_RANGE\n\nLimitation: V>0 on forward; I>0 on reverse", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.volts_to_kw.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.volts_to_kw.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/awg-to-mm": { "post": { "operationId": "calculate_electrical_awg_to_mm", "summary": "AWG to mm / mm²", "description": "Look up American Wire Gauge geometry: unrounded ASTM B258 geometric progression (primary) plus Table 1 SI standard nominals for integer 4/0–56; copper resistance at 20 °C; educational NFPA 70–style ampacity reference (edition not pinned). Accepts 12, 1/0, 4/0, or legacy −3…0. (calculation_version 1.5.0)\n\nSemantic capability: `electrical.awg_to_mm`.\n\nCalculation version: `1.5.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Solid round conductor geometric model (ASTM B258-18(2026); 2026 reapproval of B258-18)\n\nLimitation: Primary geometry is unrounded geometric progression (formula_derived); ASTM Table 1 SI nominals are a separate standard_nominal track for integer 4/0–56\n\nLimitation: Not stranded equivalent area or insulated OD\n\nLimitation: Copper Ω/km is a 20 °C material model, not AWG geometry\n\nLimitation: Ampacity is an educational NFPA 70–style thermal reference (table-like 310.16, edition not pinned); copper 14–4/0 include 60/75/90 °C; 16 AWG and finer not tabulated; not jurisdiction-usable and not a branch-circuit rating\n\nLimitation: CVP numeric goldens cover AWG diameter/area geometry; resistance is a 20 °C IACS material model; ampacity is dataset-integrity only, not NEC compliance\n\nLimitation: Integer 4/0 (−3) through 56 = standard_range + formula_derived (+ standard_nominal); non-integer n in that span → AWG_NONSTANDARD_GAUGE + formula_interpolation; n outside the span → AWG_OUTSIDE_STANDARD_RANGE + formula_extrapolation\n\nLimitation: Missing/empty awg → MISSING_REQUIRED_INPUT (empty is not AWG 0 / 1/0)\n\nLimitation: Unparseable awg → INVALID_NUMBER; field not mm|mm2 → INVALID_MODE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.0" ] }, "description": "Pin calculation_version (published: 1.5.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.awg_to_mm.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.0", "examples": [ "1.5.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.awg_to_mm.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/wire-gauge-chart": { "post": { "operationId": "calculate_electrical_awg_to_mm_alias_wire_gauge_chart", "summary": "AWG to mm / mm² (wire-gauge-chart page alias)", "description": "Look up American Wire Gauge geometry: unrounded ASTM B258 geometric progression (primary) plus Table 1 SI standard nominals for integer 4/0–56; copper resistance at 20 °C; educational NFPA 70–style ampacity reference (edition not pinned). Accepts 12, 1/0, 4/0, or legacy −3…0. (calculation_version 1.5.0)\n\nSemantic capability: `electrical.awg_to_mm`.\n\nCalculation version: `1.5.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Solid round conductor geometric model (ASTM B258-18(2026); 2026 reapproval of B258-18)\n\nLimitation: Primary geometry is unrounded geometric progression (formula_derived); ASTM Table 1 SI nominals are a separate standard_nominal track for integer 4/0–56\n\nLimitation: Not stranded equivalent area or insulated OD\n\nLimitation: Copper Ω/km is a 20 °C material model, not AWG geometry\n\nLimitation: Ampacity is an educational NFPA 70–style thermal reference (table-like 310.16, edition not pinned); copper 14–4/0 include 60/75/90 °C; 16 AWG and finer not tabulated; not jurisdiction-usable and not a branch-circuit rating\n\nLimitation: CVP numeric goldens cover AWG diameter/area geometry; resistance is a 20 °C IACS material model; ampacity is dataset-integrity only, not NEC compliance\n\nLimitation: Integer 4/0 (−3) through 56 = standard_range + formula_derived (+ standard_nominal); non-integer n in that span → AWG_NONSTANDARD_GAUGE + formula_interpolation; n outside the span → AWG_OUTSIDE_STANDARD_RANGE + formula_extrapolation\n\nLimitation: Missing/empty awg → MISSING_REQUIRED_INPUT (empty is not AWG 0 / 1/0)\n\nLimitation: Unparseable awg → INVALID_NUMBER; field not mm|mm2 → INVALID_MODE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.0" ] }, "description": "Pin calculation_version (published: 1.5.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.awg_to_mm.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.0", "examples": [ "1.5.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.awg_to_mm.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/swg-to-mm": { "post": { "operationId": "calculate_electrical_swg_to_mm", "summary": "SWG to mm / mm²", "description": "Convert Standard Wire Gauge to diameter (mm) or cross-section (mm²). (calculation_version 1.3.1)\n\nSemantic capability: `electrical.swg_to_mm`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Lookup table only for integer SWG 7/0 (−6) through 50\n\nLimitation: Out-of-range → SWG_OUT_OF_RANGE (not 0 mm)\n\nLimitation: Non-integer → SWG_NOT_INTEGER (not Math.round)\n\nLimitation: Canonical diameter is inch; mm = inch × 25.4 (exact); area uses that mm\n\nLimitation: SWG ≠ AWG; same number different diameter", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.swg_to_mm.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.swg_to_mm.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mah-to-wh": { "post": { "operationId": "calculate_electrical_mah_to_wh", "summary": "mAh to Wh", "description": "Convert battery capacity in milliamp-hours and voltage to watt-hours. (calculation_version 1.3.1)\n\nSemantic capability: `electrical.mah_to_wh`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ignores charge/discharge efficiency and Peukert effects\n\nLimitation: V ≤ 0 → VOLTAGE_MUST_BE_POSITIVE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.mah_to_wh.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.mah_to_wh.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/battery-runtime": { "post": { "operationId": "calculate_electrical_battery_runtime", "summary": "Battery runtime", "description": "Estimate constant-load battery runtime from capacity, voltage, load (W load-side or A battery-side), DoD, and load-side efficiency (watts mode); optional u_* compose expanded uncertainty on t_h via Uncertainty Engine. (calculation_version 1.2.1)\n\nSemantic capability: `electrical.battery_runtime`.\n\nCalculation version: `1.2.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant-load idealization only — not Peukert, temperature, or BMS cutoffs\n\nLimitation: Not a substitute for manufacturer runtime curves or pack design\n\nLimitation: Amps mode = battery-side discharge current; η does not enter runtime\n\nLimitation: capacity_Ah XOR capacity_mAh; both → INVALID_INPUT\n\nLimitation: Missing capacity → MISSING_REQUIRED_INPUT; P_W/I_A ≤ 0 → LOAD_MUST_BE_POSITIVE\n\nLimitation: dod/eta outside (0,1] → FRACTION_OUT_OF_RANGE\n\nLimitation: mode=watts requires P_W; mode=amps requires I_A\n\nLimitation: Optional u_* use GUM sensitivity only (no MC/ρ/νeff UI); empty u_* preserves nominal-only result\n\nLimitation: Response inputs[] is mode-canonical (capacity_Ah only; amps omits eta)\n\nLimitation: Basic frozen at calculation_version 1.2.1 — Agent schema requires u_* when uncertainty_k/confidence is set; do not stack Peukert/temperature/duty-cycle into this capability", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.1" ] }, "description": "Pin calculation_version (published: 1.2.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery_runtime.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.1", "examples": [ "1.2.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery_runtime.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/rc-time-constant": { "post": { "operationId": "calculate_electrical_rc_time_constant", "summary": "RC time constant", "description": "Solve series RC time constant τ = R·C from any two of R, C, tau; also returns −3 dB frequency and common timing multiples. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rc_time_constant`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Series first-order RC only — not parallel networks or distributed RC\n\nLimitation: f_c is the ideal LPF −3 dB corner; not a filter design tool\n\nLimitation: Fewer than two inputs → NEEDS_TWO_INPUTS; non-positive → VALUE_MUST_BE_POSITIVE\n\nLimitation: When R and C are both provided, tau is recomputed from R·C", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rc_time_constant.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rc_time_constant.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/rlc-resonance": { "post": { "operationId": "calculate_electrical_rlc_resonance", "summary": "RLC resonance", "description": "Compute ideal series or parallel RLC resonant frequency, Q, bandwidth, and reactance at resonance from L, C, and R. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rlc_resonance`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal lumped RLC only — not coupled coils, transmission lines, or crystal models\n\nLimitation: Parallel mode assumes ideal parallel R with L and C (no ESR/ESL)\n\nLimitation: Missing/non-positive L/C/R → MISSING_REQUIRED_INPUT / VALUE_MUST_BE_POSITIVE\n\nLimitation: Unknown mode → INVALID_MODE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rlc_resonance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rlc_resonance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mosfet-conduction-loss": { "post": { "operationId": "calculate_electrical_mosfet_conduction_loss", "summary": "MOSFET conduction loss", "description": "Compute MOSFET conduction loss from I, Rds(on), current_basis (dc / on-interval RMS / full-cycle MOSFET RMS), and optional Rds(Tj) via linear α or datasheet ratio. (calculation_version 1.2.2)\n\nSemantic capability: `electrical.mosfet.conduction_loss`.\n\nCalculation version: `1.2.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Conduction loss only — not switching, reverse recovery, or gate drive\n\nLimitation: Rds(Tj) is optional first-order linear or datasheet-ratio — not a physics compact model\n\nLimitation: Default α = 0.006 /°C is a Si MOSFET planning default, not manufacturer validated\n\nLimitation: current_basis selects the I definition; mixing full-cycle RMS with D double-counts duty\n\nLimitation: V_drop is I·Rds_Tj at the entered current, not a measured VDS(on) waveform point\n\nLimitation: Missing/non-positive I/Rds → MISSING_REQUIRED_INPUT / VALUE_MUST_BE_POSITIVE; D outside (0,1] → FRACTION_OUT_OF_RANGE; unknown current_basis or temperature_model → INVALID_MODE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.2" ] }, "description": "Pin calculation_version (published: 1.2.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.conduction_loss.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.2", "examples": [ "1.2.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.conduction_loss.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/uncertainty-propagate": { "post": { "operationId": "calculate_engineering_uncertainty_propagate", "summary": "Uncertainty propagation", "description": "Propagate standard uncertainties: GUM linear (binary/sensitivity/RSS/budget) or Monte Carlo (JCGM 101); optional correlations, contributions, νeff, Student-t/percentile coverage → U. (calculation_version 1.9.8)\n\nSemantic capability: `engineering.uncertainty.propagate`.\n\nCalculation version: `1.9.8`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Linear GUM (binary/sensitivity/RSS/budget) or Monte Carlo (JCGM 101) with normal/rectangular draws; not adaptive/MCMC\n\nLimitation: MC: N in 100…100000 (default 10000), deterministic Mulberry32 seed; confidence → empirical percentiles; k → U=k·u_c\n\nLimitation: budget/sensitivity Type A/B + distributions are metadata (except MC uses distribution for draws); u is standard uncertainty\n\nLimitation: contributions are diagonal (c·u)² fractions for linear modes; with correlations percents may not sum to 100%\n\nLimitation: Product/quotient use absolute first-order forms in linear mode; MC quotient rejects >5% near-zero denominator draws (MONTECARLO_UNSTABLE)\n\nLimitation: n×n correlation matrix not positive semidefinite → CORRELATION_MATRIX_NOT_PSD (singular PSD allowed); duplicate unordered pair → DUPLICATE_CORRELATION; conflicting ρ for the same pair → CONFLICTING_CORRELATION\n\nLimitation: Optional Quantity Engine v1.1: SI-prefix conversion + electrical derived rewrites (1000 mV + 2 V → 3 V; V/A → Ω; A·Ω → V; V×A → VA); different additive dimensions → UNIT_MISMATCH; not full SI algebra\n\nLimitation: Unknown mode → INVALID_MODE; k and confidence together → INVALID_INPUT\n\nLimitation: confidence with nonzero ρ/correlations → CORRELATED_DOF_NOT_SUPPORTED (use fixed k)\n\nLimitation: MC rectangular + correlation → CORRELATED_NON_NORMAL_MC_NOT_SUPPORTED (normal marginals only)\n\nLimitation: Public Agent schema uses canonical field names only (components.u/c/x; correlations i/j as index or name). Runtime still accepts legacy aliases (ua/uncertainty/sensitivity/value) for compatibility.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.9.8" ] }, "description": "Pin calculation_version (published: 1.9.8); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.propagate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.9.8", "examples": [ "1.9.8" ] } } }, "example": { "inputs": {}, "calculation_version": "1.9.8" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.propagate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pcb-trace-width": { "post": { "operationId": "calculate_electrical_pcb_trace_width", "summary": "PCB trace width", "description": "Size PCB copper traces or check ampacity with the IPC-2221 I = k·ΔT^0.44·A^0.725 relation for external and internal layers; optional u_* compose expanded uncertainty on width or I via Uncertainty Engine. (calculation_version 1.1.1)\n\nSemantic capability: `electrical.pcb.trace_width`.\n\nCalculation version: `1.1.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: IPC-2221 closed form only — not IPC-2152 chart interpolation\n\nLimitation: 1 oz/ft² modeled as 1.378 mil thickness\n\nLimitation: Bad mode/layer → INVALID_MODE; non-positive → VALUE_MUST_BE_POSITIVE\n\nLimitation: Optional u_* use GUM sensitivity on the primary result only; uncertainty_k is coverage (not IPC k)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.1" ] }, "description": "Pin calculation_version (published: 1.1.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.trace_width.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.1", "examples": [ "1.1.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.trace_width.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/lpf": { "post": { "operationId": "calculate_electrical_lpf", "summary": "Low-pass filter", "description": "Solve first-order RC LPF cutoff fc = 1/(2πRC) from any two of R, C, fc; optional magnitude |H(f)| in linear and dB. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.lpf`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: First-order passive RC LPF only\n\nLimitation: Fewer than two of R/C/fc → NEEDS_TWO_INPUTS\n\nLimitation: When R and C both provided, fc is recomputed", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.lpf.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.lpf.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/fspl": { "post": { "operationId": "calculate_electrical_rf_fspl", "summary": "Free-space path loss", "description": "Compute Friis free-space path loss from distance and frequency, with optional antenna gains Gt/Gr in dBi. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rf.fspl`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal free-space only — no atmosphere, multipath, or cable loss\n\nLimitation: d_m/f_Hz ≤ 0 → VALUE_MUST_BE_POSITIVE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.fspl.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.fspl.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mosfet-switching-loss": { "post": { "operationId": "calculate_electrical_mosfet_switching_loss", "summary": "MOSFET switching loss", "description": "First-order hard-switching overlap loss P_sw = ½·Vds·Id·(tr+tf)·f_sw and optional gate-drive power Qg·Vdrive·f_sw. Not a full MOSFET loss stack. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.mosfet.switching_loss`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Hard-switching linear transition only — not soft-switching or Eon/Eoff tables\n\nLimitation: Qg and Vdrive must both be present or both omitted (else NEEDS_TWO_INPUTS)\n\nLimitation: Conduction loss is a separate capability\n\nLimitation: P_gate is gate-drive power — not necessarily dissipated entirely in the MOSFET junction", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.switching_loss.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.switching_loss.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mosfet-total-loss": { "post": { "operationId": "calculate_electrical_mosfet_total_loss", "summary": "MOSFET total loss", "description": "Compose MOSFET loss workspace: device dissipation (conduction + hard-switching + optional Coss/Eoss) plus optional gate-drive and Qrr commutation, with optional Tj = Ta + P_device·Rth. Omitted optional terms are not treated as 0 W. (calculation_version 1.1.2)\n\nSemantic capability: `electrical.mosfet.total_loss`.\n\nCalculation version: `1.1.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: First-order hard-switching workspace — not Eon/Eoff tables, Qoss(V) curves, or compact models\n\nLimitation: Conduction uses electrical.mosfet.conduction_loss; switching/gate use electrical.mosfet.switching_loss\n\nLimitation: Default α = 0.006 /°C is a Si planning default, not manufacturer validated\n\nLimitation: P_coss from ½·Coss·V²·f is a lumped equivalent — prefer datasheet Eoss at Vds\n\nLimitation: Overlap P_sw plus P_coss may overestimate due to double counting; first-order only — validate against measured Eon/Eoff\n\nLimitation: P_rr = Qrr·Vds·f is recovered-charge commutation loss, usually attributed to the complementary switch — not this die\n\nLimitation: P_gate is gate-drive power (driver + Rg + Rg,int) — not MOSFET junction dissipation; Tj_est uses P_device only\n\nLimitation: Tj_est is steady-state RthJA only — not Zth or CFD\n\nLimitation: Numeric 0 on omitted P_gate/P_coss/P_rr means not included (see terms_omitted), not a measured zero\n\nLimitation: Optional Qg/Coss/Eoss/Qrr if present must be > 0; explicit 0 is not yet a supported known-zero state\n\nLimitation: Qg and Vdrive must both be present or both omitted (else NEEDS_TWO_INPUTS)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.2" ] }, "description": "Pin calculation_version (published: 1.1.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.total_loss.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.2", "examples": [ "1.1.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.total_loss.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/battery-runtime-temp": { "post": { "operationId": "calculate_electrical_battery_runtime_temp", "summary": "Battery runtime with temperature", "description": "Constant-load battery runtime with a generic cold-derating temperature capacity factor about 25 °C (extends Battery Runtime base: watts load-side / amps battery-side). Planning model — not chemistry. (calculation_version 1.2.1)\n\nSemantic capability: `electrical.battery.runtime_temp`.\n\nCalculation version: `1.2.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Generic cold-derating planning model by default — not Peukert, Arrhenius, or manufacturer curves\n\nLimitation: Default k_T=0.006 is a planning default (parameter_validated=false), not a validated chemistry coefficient\n\nLimitation: Clamp is a numerical safeguard, not an operating-temperature envelope\n\nLimitation: T≥25 °C under generic_cold_derating does not increase capacity (no high-temp bonus)\n\nLimitation: custom_symmetric_linear is advanced opt-in and still a first-order heuristic\n\nLimitation: Amps mode = battery-side current; η does not enter runtime\n\nLimitation: capacity_Ah XOR capacity_mAh; both → INVALID_INPUT\n\nLimitation: k_T < 0 → VALUE_MUST_BE_NON_NEGATIVE\n\nLimitation: Intermediate layer toward chemistry/manufacturer profile runtime — not a Battery Simulator", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.1" ] }, "description": "Pin calculation_version (published: 1.2.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery.runtime_temp.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.1", "examples": [ "1.2.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery.runtime_temp.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/parallel-resistor": { "post": { "operationId": "calculate_electrical_parallel_resistor", "summary": "Parallel resistor", "description": "Equivalent resistance of N≥2 parallel resistors: 1/Req = Σ 1/Ri. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.parallel_resistor`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Parallel only\n\nLimitation: N<2 → NEEDS_TWO_INPUTS", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.parallel_resistor.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.parallel_resistor.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pcb-microstrip": { "post": { "operationId": "calculate_electrical_pcb_microstrip", "summary": "Microstrip impedance", "description": "IPC-2141 / Hammerstad zero-thickness microstrip Z0 or width synthesis. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.pcb.microstrip`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Zero thickness; no soldermask\n\nLimitation: er≤1 → ER_MUST_BE_GT_1", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.microstrip.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.microstrip.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pcb-via-current": { "post": { "operationId": "calculate_electrical_pcb_via_current", "summary": "Via current capacity", "description": "IPC-2221 via ampacity from plating cross-section A=πt(d−t). (calculation_version 1.0.0)\n\nSemantic capability: `electrical.pcb.via_current`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: IPC-2221 closed form\n\nLimitation: t≥d/2 → PLATING_TOO_THICK", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.via_current.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.via_current.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/rf-link-budget": { "post": { "operationId": "calculate_electrical_rf_link_budget", "summary": "RF link budget", "description": "Friis FSPL link budget with gains, misc loss, received power, and optional margin; optional u_* compose expanded uncertainty on Pr_dBm via Uncertainty Engine. (calculation_version 1.1.1)\n\nSemantic capability: `electrical.rf.link_budget`.\n\nCalculation version: `1.1.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal free space only\n\nLimitation: Extends electrical.rf.fspl\n\nLimitation: Optional u_* use GUM sensitivity on Pr only (no MC/ρ/νeff UI); empty u_* preserves 1.0.0 fields", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.1" ] }, "description": "Pin calculation_version (published: 1.1.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.link_budget.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.1", "examples": [ "1.1.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.link_budget.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/battery-pack-sizing": { "post": { "operationId": "calculate_electrical_battery_pack_sizing", "summary": "Battery pack sizing", "description": "Invert BatteryRuntimeBaseInput constant-load model to size Ah from runtime/load (watts load-side / amps battery-side); optional nominal Ns/Np packing estimate. (calculation_version 1.2.0)\n\nSemantic capability: `electrical.battery.pack_sizing`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant-load inverse of BatteryRuntimeBaseInput / battery_runtime 1.2+\n\nLimitation: Amps mode = battery-side current; η does not enter Ah\n\nLimitation: Cell Ns/Np use ceil — nominal packing estimate only, not BMS / chemistry pack design\n\nLimitation: When V_pack ≠ V_target the result includes warning PACK_VOLTAGE_DIFFERS_FROM_TARGET\n\nLimitation: mode=watts requires P_W; mode=amps requires I_A\n\nLimitation: V_cell XOR incomplete pair → NEEDS_TWO_INPUTS (both or neither)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery.pack_sizing.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery.pack_sizing.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/wheatstone-bridge": { "post": { "operationId": "calculate_electrical_wheatstone", "summary": "Wheatstone bridge", "description": "Four-arm Wheatstone bridge Vout and balance from Vin and R1…R4. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.wheatstone`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Unloaded ideal bridge only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.wheatstone.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.wheatstone.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kirchhoff": { "post": { "operationId": "calculate_electrical_kirchhoff", "summary": "Kirchhoff's laws", "description": "Series KVL loop or parallel KCL node with N resistors. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.kirchhoff`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Single loop/node demo only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.kirchhoff.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.kirchhoff.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/led-resistor": { "post": { "operationId": "calculate_electrical_led_resistor", "summary": "LED resistor", "description": "Series LED current-limit resistor R=(Vs−n·Vf)/If. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.led_resistor`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Vs ≤ n·Vf → SUPPLY_TOO_LOW", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.led_resistor.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.led_resistor.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mosfet-tj": { "post": { "operationId": "calculate_electrical_mosfet_tj", "summary": "MOSFET junction temperature", "description": "Steady-state Tj = Ta + P·Rth. Effective RθJA, or case/heatsink-dominant RθJC+RθCA (not equivalent models). Mixing both paths is CONFLICTING_INPUTS. (calculation_version 1.1.2)\n\nSemantic capability: `electrical.mosfet.tj`.\n\nCalculation version: `1.1.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Steady-state only; not Zth or CFD\n\nLimitation: Rth_JA is effective/application RθJA for the user's PCB and cooling environment, not a universal JEDEC package constant\n\nLimitation: JC+CA is a case/heatsink-dominant lumped single-path approximation; it is not a universal equivalent of RθJA and ignores parallel PCB/package heat flow\n\nLimitation: Rth_JA and Rth_JC or Rth_CA together is schema-invalid and CONFLICTING_INPUTS", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.2" ] }, "description": "Pin calculation_version (published: 1.1.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.tj.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.2", "examples": [ "1.1.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.tj.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cascaded-nf": { "post": { "operationId": "calculate_electrical_rf_cascaded_nf", "summary": "Cascaded noise figure", "description": "Friis cascaded NF and total gain from stage NF/G in dB. (calculation_version 1.1.1)\n\nSemantic capability: `electrical.rf.cascaded_nf`.\n\nCalculation version: `1.1.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Mismatch effects are not modeled\n\nLimitation: Image-noise / special mixer sideband behavior is not modeled\n\nLimitation: REST/MCP arrays NF_dB[]/G_dB[] are limited to 64 stages (TOO_MANY_STAGES); field encoding NF1…NF8 is limited to 8\n\nLimitation: Field encoding and array encoding are mutually exclusive (MIXED_INPUT_ENCODING); field stages must be contiguous from stage 1 (NONCONTIGUOUS_STAGES)\n\nLimitation: When 10^(G_tot_dB/10) overflows IEEE-754 binary64, G_tot_lin is null and LINEAR_GAIN_OVERFLOW is returned; G_tot_dB remains finite", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.1" ] }, "description": "Pin calculation_version (published: 1.1.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.cascaded_nf.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.1", "examples": [ "1.1.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.cascaded_nf.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/current-divider": { "post": { "operationId": "calculate_electrical_current_divider", "summary": "Current divider", "description": "Two-branch parallel current divider. Web UI: It, R1, R2 → I1, I2, V. API also solves selected inverse combinations (not arbitrary any-three; It+I1+I2 is underdetermined). (calculation_version 1.0.2)\n\nSemantic capability: `electrical.current_divider`.\n\nCalculation version: `1.0.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exactly two ideal resistive parallel branches; no additional branch or load\n\nLimitation: Currents are non-negative magnitudes\n\nLimitation: Web UI is It+R1+R2 only\n\nLimitation: API supported combinations: It+R1+R2, R1+R2+I1, R1+R2+I2, It+I1+R1, It+I1+R2\n\nLimitation: It+I1+I2 is underdetermined → UNSUPPORTED_COMBINATION\n\nLimitation: Inverse It+I1+R1/R2 requires 0 < I1 < It for a finite R>0; I1=0 or I1=It → CURRENT_SPLIT_INVALID\n\nLimitation: It=0 and I1=0 with R1 or R2 is underdetermined → UNSUPPORTED_COMBINATION\n\nLimitation: <3 inputs → NEEDS_THREE_INPUTS", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.2" ] }, "description": "Pin calculation_version (published: 1.0.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.current_divider.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.2", "examples": [ "1.0.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.current_divider.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hpf": { "post": { "operationId": "calculate_electrical_hpf", "summary": "High-pass filter", "description": "First-order RC HPF cutoff and optional |H(f)|. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.hpf`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: First-order RC only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.hpf.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.hpf.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vswr": { "post": { "operationId": "calculate_electrical_rf_vswr", "summary": "VSWR", "description": "Convert |Γ|, VSWR, and return loss (plus mismatch loss). (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rf.vswr`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Scalar |Γ| only\n\nLimitation: |Γ|≥1 → GAMMA_OUT_OF_RANGE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.vswr.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.vswr.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/tolerance-stackup": { "post": { "operationId": "calculate_engineering_tolerance_stackup", "summary": "Tolerance stack-up", "description": "1-D RSS or worst-case tolerance stack — Basic tol list or Engineering dimensions (nominal, ±tol, direction). (calculation_version 1.4.0)\n\nSemantic capability: `engineering.tolerance.stackup`.\n\nCalculation version: `1.4.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: 1-D linear stack only — not geometric GD&T or Monte Carlo\n\nLimitation: Basic inputs are treated as comparable tolerance magnitudes, not automatically as 1σ / 3σ / drawing limits\n\nLimitation: RSS is a statistical estimate under independence; it is not a guaranteed assembly limit\n\nLimitation: Engineering statistical_basis: magnitude (default, no coverage) and 1sigma use a; 3sigma uses a/3; uniform uses a/√3\n\nLimitation: Uniform asymmetric ±tol shifts statistical center to interval midpoint (NIST Type B rectangular); stack_nom stays drawing nominal\n\nLimitation: Legacy distribution=normal→1sigma, unknown→magnitude, uniform→uniform\n\nLimitation: stack_half_range is not a hard worst-case bound when +Tol/−Tol are asymmetric about nominal — use stack_worst_plus / stack_worst_minus", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.4.0" ] }, "description": "Pin calculation_version (published: 1.4.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.tolerance.stackup.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.4.0", "examples": [ "1.4.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.4.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.tolerance.stackup.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/opamp-error-budget": { "post": { "operationId": "calculate_electrical_opamp_error_budget", "summary": "Op-amp error budget", "description": "DC Vos/Ib/Ios error budget with Rf/Rg (RSS or worst-case). (calculation_version 1.0.0)\n\nSemantic capability: `electrical.opamp.error_budget`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: DC Vos/Ib/Ios only — not noise/CMRR/PSRR", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.opamp.error_budget.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.opamp.error_budget.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/opamp-gain": { "post": { "operationId": "calculate_electrical_opamp_gain", "summary": "Op-amp gain", "description": "Closed-loop non-inverting / inverting gain from Rf and Rg. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.opamp_gain`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal DC closed-loop only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.opamp_gain.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.opamp_gain.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/antenna-length": { "post": { "operationId": "calculate_electrical_rf_antenna_length", "summary": "Antenna length", "description": "λ/2 dipole total length · λ/4 monopole radiator · corrected 1λ (k·λ₀) from frequency and empirical length factor k. (calculation_version 1.0.3)\n\nSemantic capability: `electrical.rf.antenna_length`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not a full antenna model — no ground, diameter, end-effect, loading coils, or NEC geometry.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.antenna_length.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.antenna_length.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ac-dc-rectifier": { "post": { "operationId": "calculate_electrical_ac_dc_rectifier", "summary": "AC↔DC rectifier", "description": "Ideal half/full-wave rectified waveform (Vpeak/Vavg/Vrms) or capacitor-smoothed DC estimate — two circuit models. (calculation_version 1.1.2)\n\nSemantic capability: `electrical.ac_dc_rectifier`.\n\nCalculation version: `1.1.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal diodes (0 V drop); not SCR/thyristor or active PFC\n\nLimitation: Vavg is the unfiltered rectified-sine average, not capacitor-smoothed DC bus voltage\n\nLimitation: Capacitor model uses continuous-discharge ΔV≈I/(f_ripple·C); when ΔV≥Vpeak, Vdc_est and Vmin are withheld (model_validity.valid=false)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.2" ] }, "description": "Pin calculation_version (published: 1.1.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.ac_dc_rectifier.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.2", "examples": [ "1.1.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.ac_dc_rectifier.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/adc-error-budget": { "post": { "operationId": "calculate_electrical_adc_error_budget", "summary": "ADC error budget", "description": "Combine gain/offset/INL/DNL into LSB, volts, and %FS. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.adc.error_budget`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Static DC errors only.\n\nLimitation: Quantization ±0.5 LSB is separate unless included in the INL/DNL terms you enter.\n\nLimitation: CalculatorX includes DNL as a separate RSS/worst-case contributor. Some ADC datasheets define TUE using gain, offset, and INL only.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.adc.error_budget.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.adc.error_budget.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pcb-diff-impedance": { "post": { "operationId": "calculate_electrical_pcb_diff_impedance", "summary": "Differential impedance", "description": "Edge-coupled microstrip Zdiff from W, H, S, εr. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.pcb.diff_impedance`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Zero copper thickness (T=0); homogeneous dielectric; no soldermask\n\nLimitation: S_m is edge-to-edge gap, not center-to-center\n\nLimitation: Not a field solver; omits dielectric dispersion, copper roughness, and weave", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.diff_impedance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.diff_impedance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/capacitance": { "post": { "operationId": "calculate_electrical_capacitance", "summary": "Capacitance", "description": "Parallel-plate and series/parallel capacitance. (calculation_version 1.1.0)\n\nSemantic capability: `electrical.capacitance`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal parallel plates; homogeneous isotropic dielectric fully filling the gap; fringing, frequency dependence, dielectric loss, leakage, ESR/ESL and parasitics neglected", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.capacitance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.capacitance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/transformer-sizing": { "post": { "operationId": "calculate_electrical_transformer_sizing", "summary": "Transformer sizing", "description": "Ideal transformer ratio, current, and VA. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.transformer_sizing`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal lossless single-phase", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.transformer_sizing.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.transformer_sizing.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/diode-equation": { "post": { "operationId": "calculate_electrical_diode_equation", "summary": "Diode equation", "description": "Shockley diode Id↔Vd. Canonical T_K; UI/query alias T_C. Defaults: mode=id, n=1, T_K=300. Inverse domain Id > -Is. (calculation_version 1.1.0)\n\nSemantic capability: `electrical.diode.equation`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal Shockley; no Rs/breakdown/high-injection\n\nLimitation: Is is specified at T; Is(T) is not derived\n\nLimitation: mode=vd requires Id > -Is\n\nLimitation: binary64 overflow → NUMERIC_OVERFLOW", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.diode.equation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.diode.equation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/adc-snr": { "post": { "operationId": "calculate_electrical_adc_snr", "summary": "ADC SNR / ENOB", "description": "Ideal quantization SNR and ENOB from measured SINAD. (calculation_version 1.1.0)\n\nSemantic capability: `electrical.adc.snr`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal quantization only. ENOB from measured SINAD, not SNR.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.adc.snr.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": { "mode": "snr", "n_bits": 12 }, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.adc.snr.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pcb-stripline": { "post": { "operationId": "calculate_electrical_pcb_stripline", "summary": "Stripline impedance", "description": "Symmetric stripline Z0 from W, b, εr. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.pcb.stripline`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Zero thickness approximation", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.stripline.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.stripline.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/dbm-watt": { "post": { "operationId": "calculate_units_rf_dbm_watts", "summary": "dBm to Watts", "description": "Convert dBm ↔ watts / milliwatts using log power ratios. (calculation_version 1.3.1)\n\nSemantic capability: `units.rf.dbm_watts`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: W/mW must be >0 for reverse log\n\nLimitation: Hard INVALID_MODE\n\nLimitation: IEEE-754 binary64 overflow → NUMERIC_OVERFLOW\n\nLimitation: IEEE-754 binary64 underflow to 0 → NUMERIC_UNDERFLOW", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.rf.dbm_watts.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": { "mode": "dbm-w", "value": 30 }, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.rf.dbm_watts.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/worst-case-analysis": { "post": { "operationId": "calculate_engineering_tolerance_worst_case", "summary": "Worst-Case Tolerance Analysis", "description": "1-D linear worst-case tolerance magnitude stack Σ|tol| with RSS comparison (|cᵢ|=1). (calculation_version 1.3.0)\n\nSemantic capability: `engineering.tolerance.worst_case`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: 1-D linear magnitude stack only — not a full nominal min/max dimensional chain\n\nLimitation: RSS comparison assumes consistent statistical basis and independence\n\nLimitation: MCP/agent input schema is canonical (tolerances[] ≥ 0); REST still accepts tol[] / tol1…tol8\n\nLimitation: Canonical/UI magnitudes must be ≥ 0 (NEGATIVE_TOLERANCE_MAGNITUDE). REST signed values ignore sign (SIGN_IGNORED_FOR_TOLERANCE_MAGNITUDE)\n\nLimitation: Unit is a shared label; all contributors must already use the same unit — no conversion", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.tolerance.worst_case.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": { "tolerances": [ 0.1, 0.2, 0.1 ], "unit": "mm" }, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.tolerance.worst_case.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/series-capacitor": { "post": { "operationId": "calculate_electrical_series_capacitor", "summary": "Series Capacitor", "description": "Series equivalent capacitance 1/C=Σ1/Ci. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.series_capacitor`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal capacitors", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.series_capacitor.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.series_capacitor.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/timer-555": { "post": { "operationId": "calculate_electrical_timer_555", "summary": "555 Timer", "description": "Astable frequency/duty/timing and monostable pulse width for the classic 555 using ln(2)-canonical NE555 timing (TI 0.693/1.44 are documented rounded aliases). (calculation_version 1.2.0)\n\nSemantic capability: `electrical.timer_555`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Classic NE555 ideal timing — astable uses ln(2) canonical model; TI 0.693/1.44 are rounded aliases\n\nLimitation: Device families differ in timing accuracy, leakage, output/discharge characteristics and usable frequency range; verify the selected device datasheet\n\nLimitation: Standard astable wiring always yields duty > 50%; diode-across-R2 <50% trick is not modeled\n\nLimitation: f > 100 kHz → NE555_HIGH_FREQUENCY warning (NE555 distortion guidance)\n\nLimitation: Monostable pulse_width < ~10 µs → MONOSTABLE_SHORT_PULSE warning\n\nLimitation: mode-discriminated oneOf: astable requires R1,R2,C; monostable requires R,C\n\nLimitation: Frozen at calculation_version 1.2.0 for forward timing — Designer / E-series / tolerance are separate surfaces", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.timer_555.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.timer_555.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/skin-depth": { "post": { "operationId": "calculate_electrical_rf_skin_depth", "summary": "Skin Depth", "description": "Electromagnetic skin depth δ=√(ρ/(πfμ)). (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rf.skin_depth`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Good-conductor approximation", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.skin_depth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.skin_depth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/process-capability": { "post": { "operationId": "calculate_engineering_process_capability", "summary": "Process Capability (Cp/Cpk)", "description": "Design-stage Cp/Cpk from μ, σ, LSL, USL. Not in-control SPC and not Monte Carlo simulated indices. (calculation_version 1.0.0)\n\nSemantic capability: `engineering.process.capability`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Design-stage indices from μ and σ — not measured in-control SPC\n\nLimitation: Not Monte Carlo simulated Cp/Cpk\n\nLimitation: Two-sided LSL/USL required; USL must be greater than LSL", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.capability.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "lsl": 0, "usl": 12, "mu": 6, "sigma": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.capability.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cpm": { "post": { "operationId": "calculate_engineering_process_cpm", "summary": "Process capability (Cpm)", "description": "Taguchi Cpm = (USL−LSL)/(6√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and a target. Not Cp/Cpk, not Pp/Ppk, and not a Cpm≥1.33 verdict. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.process.cpm`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Design-stage from stated μ and σ — not measured in-control SPC\n\nLimitation: Not Cp/Cpk (those ignore the target in the denominator)\n\nLimitation: Not Pp/Ppk (those use sample s and have no target)\n\nLimitation: This page does not issue a Cpm≥1.33 verdict", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpm.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "lsl": 0, "usl": 12, "mu": 6, "sigma": 1, "target": 6 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpm.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cpm-performance": { "post": { "operationId": "calculate_engineering_process_cpm_performance", "summary": "Process performance (Ppm)", "description": "Overall Taguchi Ppm = (USL−LSL)/(6√(s²+(x̄−target)²)) from a sample. Not design-stage Cpm, not Pp/Ppk, and not a Ppm≥1.33 verdict. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.process.cpm_performance`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Overall sample s — not design-stage Cpm from a stated σ\n\nLimitation: Not Pp/Ppk (those have no target in the denominator)\n\nLimitation: This page does not issue a Ppm≥1.33 verdict", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpm_performance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "values": [ 4, 6, 8 ], "lsl": 0, "usl": 12, "target": 6 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpm_performance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cpmk": { "post": { "operationId": "calculate_engineering_process_cpmk", "summary": "Process capability (Cpmk)", "description": "Taguchi Cpmk = min(USL−μ, μ−LSL)/(3√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and a target. Not Cpm, not Cpk, not Ppm, and not a Cpmk≥1.33 verdict. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.process.cpmk`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Design-stage from stated μ and σ — not measured in-control SPC\n\nLimitation: Not Cpm (that uses the two-sided span USL−LSL)\n\nLimitation: Not Cpk (Cpk has no target in the denominator)\n\nLimitation: Not Ppm (that uses sample s)\n\nLimitation: This page does not issue a Cpmk≥1.33 verdict", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpmk.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "lsl": 0, "usl": 12, "mu": 6, "sigma": 1, "target": 6 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpmk.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cpmk-performance": { "post": { "operationId": "calculate_engineering_process_cpmk_performance", "summary": "Process performance (Ppmk)", "description": "Overall Taguchi Ppmk = min(USL−x̄, x̄−LSL)/(3√(s²+(x̄−target)²)) from a sample. Not Cpmk, not Ppk, not Ppm, and not a Ppmk≥1.33 verdict. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.process.cpmk_performance`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Overall sample s — not design-stage Cpmk from a stated σ\n\nLimitation: Not Ppk (Ppk has no target in the denominator)\n\nLimitation: Not Ppm (that uses the two-sided span USL−LSL)\n\nLimitation: This page does not issue a Ppmk≥1.33 verdict", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpmk_performance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "values": [ 4, 6, 8 ], "lsl": 0, "usl": 12, "target": 6 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.cpmk_performance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/process-performance": { "post": { "operationId": "calculate_engineering_process_performance", "summary": "Process performance (Pp/Ppk)", "description": "Overall Pp/Ppk from a sample of process observations. σ is the overall sample s (ddof=1). Not design-stage Cp/Cpk, not Type A u_A, and not Monte Carlo simulated indices. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.process.performance`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Overall sample s — not a stated design σ and not within-subgroup SPC\n\nLimitation: Not design-stage Cp/Cpk and not Type A u_A = s/√n\n\nLimitation: Not Monte Carlo simulated indices\n\nLimitation: Two-sided LSL/USL required; USL must be greater than LSL", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.performance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "values": [ 4, 6, 8 ], "lsl": 0, "usl": 12 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.performance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/guard-band": { "post": { "operationId": "calculate_engineering_process_guard_band", "summary": "Guard Band", "description": "Simple guard band GB=k·u with optional acceptance limits. Not ILAC G8 / JCGM 106 risk-based decision rules. (calculation_version 1.0.0)\n\nSemantic capability: `engineering.process.guard_band`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: GB = k·u with k default 2 — not ILAC G8 / JCGM 106 risk-based rules\n\nLimitation: USL and LSL optional; omitted limits skip that acceptance output\n\nLimitation: Not Cp/Cpk and not Monte Carlo", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.guard_band.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "u": 0.5, "k": 2, "lsl": 0, "usl": 12 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.process.guard_band.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/type-a": { "post": { "operationId": "calculate_engineering_uncertainty_type_a", "summary": "Type A Uncertainty", "description": "Type A standard uncertainty u_A = s/√n from repeated observations. Not GUM combination and not Monte Carlo. (calculation_version 1.0.0)\n\nSemantic capability: `engineering.uncertainty.type_a`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Type A from a sample — not GUM RSS of several uᵢ\n\nLimitation: Not Monte Carlo\n\nLimitation: ddof=1 requires n≥2", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.type_a.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "values": [ 1, 2, 3 ], "ddof": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.type_a.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/type-b": { "post": { "operationId": "calculate_engineering_uncertainty_type_b", "summary": "Type B Uncertainty", "description": "Type B standard uncertainty from a half-width a. Rectangular u_B=a/√3, triangular u_B=a/√6. Not GUM combination and not Monte Carlo. (calculation_version 1.0.0)\n\nSemantic capability: `engineering.uncertainty.type_b`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One Type B component from a half-width — not GUM RSS of several uᵢ\n\nLimitation: Not Monte Carlo\n\nLimitation: Seeded distributions: rectangular and triangular only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.type_b.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "a": 3, "distribution": "rectangular" }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.type_b.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/type-b-nu": { "post": { "operationId": "calculate_engineering_uncertainty_type_b_nu", "summary": "Type B degrees of freedom", "description": "GUM G.4.2 Type B degrees of freedom: ν = ½(u/σ(u))². σ(u)=0 → ν is infinite. Not Type B u_B from a half-width, not Welch ν_eff, and not U = k·u_c. (calculation_version 1.0.0)\n\nSemantic capability: `engineering.uncertainty.type_b_nu`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: GUM G.4.2 ν from stated u and σ(u) — not Type B u_B = a/√3\n\nLimitation: Not Welch–Satterthwaite ν_eff from several u_i, ν_i\n\nLimitation: Not expanded U = k·u_c\n\nLimitation: Does not take half-width a", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.type_b_nu.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "u": 2, "sigma_u": 0.5 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.type_b_nu.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/welch-satterthwaite": { "post": { "operationId": "calculate_engineering_uncertainty_welch_satterthwaite", "summary": "Welch–Satterthwaite ν_eff", "description": "Effective degrees of freedom ν_eff = u_c⁴ / Σ (u_i⁴ / ν_i) (GUM G.4). If uc is omitted, u_c is the uncorrelated RSS of u_i. Not combined RSS as a product page and not expanded U = k·u_c. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.uncertainty.welch_satterthwaite`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Does not combine a measurement model (use Uncertainty propagate)\n\nLimitation: Does not look up coverage factor k from a t-table\n\nLimitation: Does not compute expanded U = k·u_c\n\nLimitation: Uncorrelated RSS only when uc is omitted", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.welch_satterthwaite.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "u": [ 1, 1 ], "nu": [ 8, 8 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.welch_satterthwaite.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/weighted-mean": { "post": { "operationId": "calculate_engineering_uncertainty_weighted_mean", "summary": "Inverse-variance weighted mean", "description": "GUM H.3 inverse-variance weighted mean of independent results of the same measurand: x_w = Σ(x_i/u_i²)/Σ(1/u_i²), u_w = 1/√Σ(1/u_i²). Not combined RSS, not Type A u_A = s/√n, and not GUM propagate. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.uncertainty.weighted_mean`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Independent uncorrelated results of the same measurand — not RSS of a measurement model\n\nLimitation: Does not compute Type A u_A = s/√n from repeats without individual u_i\n\nLimitation: Does not compute expanded U = k·u_w\n\nLimitation: χ² / Birge are diagnostics, not a pass/fail verdict", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.weighted_mean.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "x": [ 2, 4, 6, 8 ], "u": [ 1, 1, 1, 1 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.weighted_mean.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/coverage-factor": { "post": { "operationId": "calculate_engineering_uncertainty_coverage_factor", "summary": "Coverage factor k", "description": "Two-sided coverage factor k = t_{(1+p)/2}(ν) from degrees of freedom and confidence (GUM G.3 / G.4). Infinite ν uses the normal quantile. Not expanded U = k·u_c and not GUM propagate. (calculation_version 1.0.0)\n\nSemantic capability: `engineering.uncertainty.coverage_factor`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Does not compute expanded U = k·u_c (use Uncertainty propagate)\n\nLimitation: Does not combine a measurement model\n\nLimitation: Does not look up ν_eff (use Welch–Satterthwaite)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.coverage_factor.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "nu": 8, "confidence": 0.95 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.coverage_factor.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/tur": { "post": { "operationId": "calculate_engineering_uncertainty_tur", "summary": "Test uncertainty ratio TUR", "description": "Two-sided TUR = (USL−LSL)/(2U) from an already-expanded U (ANSI/NCSL Z540.3). Spec via lsl+usl, T, or half-width tol. Not pass/fail, not guard band, and not combined RSS. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.uncertainty.tur`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: U is already expanded — this page does not compute U = k·u_c\n\nLimitation: Does not combine a measurement model or RSS of u_i\n\nLimitation: Does not issue a TUR≥4 pass/fail or an ILAC G8 decision\n\nLimitation: Not a guard band and not Cp/Cpk", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.tur.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "U": 0.5, "lsl": 0, "usl": 4 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.tur.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/decision-rule": { "post": { "operationId": "calculate_engineering_conformity_decision_rule", "summary": "Conformity decision rule", "description": "Binary ILAC G8-style decision on a measured y: simple acceptance (w=0) or guarded acceptance (LSL+w ≤ y ≤ USL−w). The guard-band zone is fail, not conditional. Not JCGM 106 risk, not TUR, and not GB-only. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.conformity.decision_rule`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Binary pass/fail only — the guard-band zone is fail, not conditional\n\nLimitation: Does not compute ILAC G8 / JCGM 106 consumer or producer risk\n\nLimitation: Does not compute TUR or GB = k·u as a product (use those pages)\n\nLimitation: U or w is the already-stated band; this page does not expand u_c", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.decision_rule.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "y": 6, "lsl": 0, "usl": 12, "rule": "simple" }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.decision_rule.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mpe": { "post": { "operationId": "calculate_engineering_conformity_mpe", "summary": "Maximum permissible error MPE", "description": "VIM MPE: pass iff |ylab−xref| ≤ MPE. ratio = |ε|/MPE. Equality is pass. Not an ILAC G8 spec decision on y, not En (no U), and not ε without a limit. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.conformity.mpe`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Binary |ε| ≤ MPE — equality is pass\n\nLimitation: Does not compare y to LSL/USL (use the decision-rule page)\n\nLimitation: Does not divide by U (that is En) and does not report ε without a limit\n\nLimitation: U, Ulab, and T are not aliases for MPE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.mpe.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "ylab": 2.5, "xref": 2, "MPE": 1 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.mpe.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/normalized-error": { "post": { "operationId": "calculate_engineering_conformity_normalized_error", "summary": "Normalized error En", "description": "Proficiency-testing En = (ylab−xref)/√(Ulab²+Uref²). |En| ≤ 1 is pass (ISO 13528 / ISO/IEC 17043). Ulab and Uref are already expanded. Not zeta, not TUR, and not an ILAC G8 spec decision. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.conformity.normalized_error`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ulab and Uref are already expanded — this page does not compute U = k·u\n\nLimitation: Not the zeta-score (that uses standard u, not U)\n\nLimitation: Not TUR and not an ILAC G8 specification decision on y\n\nLimitation: |En| ≤ 1 is pass; the test does not add a warning zone", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.normalized_error.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "ylab": 2.5, "xref": 0, "Ulab": 3, "Uref": 4 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.normalized_error.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/zeta-score": { "post": { "operationId": "calculate_engineering_conformity_zeta_score", "summary": "Zeta-score", "description": "Proficiency-testing zeta-score ζ = (ylab−xref)/√(ulab²+uref²). ulab and uref are standard uncertainties (ISO 13528). |ζ| ≤ 2 pass, 2 < |ζ| < 3 warning, |ζ| ≥ 3 fail. Not En, not TUR, and not an ILAC G8 spec decision. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.conformity.zeta_score`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: ulab and uref are standard uncertainties — this page does not compute U = k·u or En\n\nLimitation: Not the normalized error En (that uses already-expanded U)\n\nLimitation: Not TUR and not an ILAC G8 specification decision on y\n\nLimitation: |ζ| ≤ 2 is pass; 2 < |ζ| < 3 is warning; |ζ| ≥ 3 is fail", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.zeta_score.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "ylab": 2.5, "xref": 0, "ulab": 3, "uref": 4 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.zeta_score.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/z-score": { "post": { "operationId": "calculate_engineering_conformity_z_score", "summary": "Proficiency-testing z-score", "description": "ISO 13528 z-score z = (ylab−xref)/σ_pt. σ_pt is the scheme standard deviation for proficiency assessment (SDPA), not laboratory u and not expanded U. |z| ≤ 2 pass, 2 < |z| < 3 warning, |z| ≥ 3 fail. Not zeta, not En, and not an ILAC G8 spec decision. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.conformity.z_score`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: σ_pt is the scheme SDPA — this page does not compute lab u or U = k·u\n\nLimitation: Not the zeta-score (that uses √(ulab²+uref²))\n\nLimitation: Not the normalized error En (that uses already-expanded U)\n\nLimitation: Not TUR and not an ILAC G8 specification decision on y\n\nLimitation: |z| ≤ 2 is pass; 2 < |z| < 3 is warning; |z| ≥ 3 is fail", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.z_score.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "ylab": 2.5, "xref": 0, "sigma": 5 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.z_score.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/z-prime": { "post": { "operationId": "calculate_engineering_conformity_z_prime", "summary": "Proficiency-testing z′", "description": "ISO 13528 z′ = (ylab−xref)/√(σ_pt²+u(x_pt)²). σ_pt and u(x_pt) must both be > 0 so this cannot wrap z-score. |z′| ≤ 2 pass, 2 < |z′| < 3 warning, |z′| ≥ 3 fail. Not z-score, not zeta, and not En. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.conformity.z_prime`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Requires σ_pt > 0 and u(x_pt) > 0 — this page does not wrap z-score\n\nLimitation: Not the z-score (that divides by σ_pt alone)\n\nLimitation: Not the zeta-score (that uses √(ulab²+uref²))\n\nLimitation: Not the normalized error En (that uses already-expanded U)\n\nLimitation: Not TUR and not an ILAC G8 specification decision on y", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.z_prime.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "ylab": 5, "xref": 0, "sigma": 3, "u_xref": 4 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.conformity.z_prime.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/measurement-error": { "post": { "operationId": "calculate_engineering_measurement_error", "summary": "Measurement error", "description": "VIM measurement error ε = ylab − xref (signed). Relative error is ε/xref when xref ≠ 0. Not percent error (×100), not En, not zeta, and not a z-score. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.measurement.error`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Signed error — this page does not multiply by 100 (that is percent error)\n\nLimitation: Not En, zeta, or z-score (those divide by U, u, or σ_pt)\n\nLimitation: Not an ILAC G8 specification decision\n\nLimitation: Relative error is undefined when xref = 0", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.error.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "ylab": 2.5, "xref": 2 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.error.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/accuracy": { "post": { "operationId": "calculate_engineering_measurement_accuracy", "summary": "Measurement bias (trueness)", "description": "VIM trueness: signed bias = x̄ − xm from repeats on a master. s may be zero. Not a single-shot measurement error, not Type A u_A, and not Type-1 Cg (no T). (calculation_version 1.0.1)\n\nSemantic capability: `engineering.measurement.accuracy`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Signed bias from a sample mean — not a single-shot measurement error ε\n\nLimitation: Does not report Type A u_A = s/√n\n\nLimitation: Does not need a tolerance T (that is Type-1 Cg/Cgk)\n\nLimitation: s = 0 is valid; n = 1 with ddof = 1 is VALUE_OUT_OF_RANGE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.accuracy.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "values": [ 6, 7, 8 ], "xm": 8 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.accuracy.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/precision": { "post": { "operationId": "calculate_engineering_measurement_precision", "summary": "Measurement precision (repeatability)", "description": "ISO 5725 repeatability from a sample: s, CV = s/|x̄| when x̄ ≠ 0, and r = 2.8·s. Not Type A u_A, not Gauge R&R EV, and not percent CV (×100). (calculation_version 1.0.1)\n\nSemantic capability: `engineering.measurement.precision`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: r = 2.8·s is the ISO 5725 conventional repeatability limit, not coverage factor k\n\nLimitation: Does not report Type A u_A = s/√n\n\nLimitation: Not Gauge R&R repeatability (EV)\n\nLimitation: CV is not multiplied by 100; CV is undefined when x̄ = 0", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.precision.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "values": [ 7, 8, 9 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.precision.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/reproducibility": { "post": { "operationId": "calculate_engineering_measurement_reproducibility", "summary": "ISO 5725 reproducibility limit", "description": "ISO 5725 reproducibility from stated components: s_R = √(s_r²+s_L²), R = 2.8·s_R. Not r = 2.8·s from a sample, not AIAG GRR, and not combined RSS of a measurement model. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.measurement.reproducibility`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Takes stated s_r and s_L — not a sample and not a single s_R wrap\n\nLimitation: Not ISO 5725 r = 2.8·s from repeats\n\nLimitation: Not AIAG Gauge R&R AV / GRR\n\nLimitation: Not combined RSS of a measurement model", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.reproducibility.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "s_r": 3, "s_L": 4 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.reproducibility.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/precision-uncertainty": { "post": { "operationId": "calculate_engineering_uncertainty_precision_mean", "summary": "Uncertainty of a mean from precision", "description": "ISO 21748 u = √(s_L²+s_r²/n) of a mean of n≥2 replicates from stated precision components. Not R = 2.8·s_R, not Type A from a sample, and not U = k·u. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.uncertainty.precision_mean`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Takes stated s_r, s_L, and n≥2 — not a sample of observations\n\nLimitation: n=1 is rejected so this cannot wrap s_R\n\nLimitation: Not ISO 5725 R = 2.8·s_R and not Type A u_A = s/√n from values\n\nLimitation: Does not compute expanded U = k·u", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.precision_mean.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "s_r": 8, "s_L": 3, "n": 4 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.precision_mean.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pooled-sd": { "post": { "operationId": "calculate_engineering_uncertainty_pooled_sd", "summary": "Pooled standard deviation", "description": "Pooled s_p = √(Σ ν_i s_i² / Σ ν_i) from k≥2 stated sample standard deviations and their degrees of freedom. Not Type A from one sample, not Welch–Satterthwaite ν_eff, and not ISO 21748 u of a mean. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.uncertainty.pooled_sd`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Takes stated s_i and ν_i — not a single sample of observations\n\nLimitation: k=1 is rejected so this cannot wrap Type A / identity s\n\nLimitation: Does not compute Welch–Satterthwaite ν_eff\n\nLimitation: Does not compute ISO 21748 u of a mean", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.pooled_sd.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "s": [ 1, 7 ], "nu": [ 1, 1 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.uncertainty.pooled_sd.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/duplicate-sd": { "post": { "operationId": "calculate_engineering_measurement_duplicate_sd", "summary": "Repeatability from duplicates", "description": "ISO 5725 repeatability s_r = √(Σ d_i² / (2m)) from m≥2 duplicate differences. Not Type A from a sample of observations, not r = 2.8·s, and not AIAG GRR EV = R̄/d2. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.measurement.duplicate_sd`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Takes duplicate differences — not a sample of observations\n\nLimitation: m=1 is rejected so this cannot wrap |d|/√2\n\nLimitation: Does not report r = 2.8·s_r\n\nLimitation: Not AIAG GRR EV = R̄/d2", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.duplicate_sd.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "d": [ 6, 8 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.duplicate_sd.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cochran": { "post": { "operationId": "calculate_engineering_measurement_cochran", "summary": "Cochran's C", "description": "ISO 5725-2 Cochran C = s_max² / Σ s_i² from k≥2 stated laboratory sample standard deviations. Not pooled s_p, not Hartley's F_max, and not a tabulated Ccrit pass/fail. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.measurement.cochran`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Takes stated laboratory s_i — not a sample of observations\n\nLimitation: k=1 is rejected so this cannot wrap identity C=1\n\nLimitation: All-zero s is rejected (Σ s² must be > 0)\n\nLimitation: Does not compare C to a tabulated Ccrit(p, n, α)\n\nLimitation: Not pooled s_p and not Hartley's F_max", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.cochran.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "s": [ 3, 4, 5 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.measurement.cochran.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gauge-capability": { "post": { "operationId": "calculate_engineering_msa_gauge_capability", "summary": "Gauge capability (Cg/Cgk)", "description": "Type-1 Cg/Cgk from repeats on a master: Cg=(frac·T)/(6s), Cgk=(frac·T/2−|x̄−xm|)/(3s). frac defaults to 0.2 (Bosch / VDA 5). Not AIAG GRR, not Cp/Cpk, and not a Cg≥1.33 verdict. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.msa.gauge_capability`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Type-1 study on a master — not AIAG GRR compose (EV/AV/PV)\n\nLimitation: Not process Cp/Cpk or Pp/Ppk\n\nLimitation: Does not issue a Cg≥1.33 pass/fail\n\nLimitation: frac is a tolerance fraction (default 0.2), not coverage factor k", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.gauge_capability.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "values": [ 7, 8, 9 ], "xm": 8, "T": 30 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.gauge_capability.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/linearity": { "post": { "operationId": "calculate_engineering_msa_linearity", "summary": "MSA linearity", "description": "OLS of measurement error ε = ylab − xref versus xref: slope = dε/d(xref). n≥3 paired points. Not a single-master bias, not Type-1 Cg, and not a %Linearity pass/fail. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.msa.linearity`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ordinary least squares of ε versus xref — not a %Linearity / process-variation verdict\n\nLimitation: Not a single-master bias (Accuracy) and not Type-1 Cg/Cgk\n\nLimitation: Does not take T and does not issue pass/fail\n\nLimitation: n≥3 paired points; xref must not all be equal", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.linearity.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "xref": [ 0, 2, 4 ], "ylab": [ 0, 3, 6 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.linearity.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hysteresis": { "post": { "operationId": "calculate_engineering_msa_hysteresis", "summary": "MSA hysteresis", "description": "VIM / MSA hysteresis: H = max |y_up − y_down| at index-paired stations. n≥2. Not OLS linearity, not a %Hysteresis pass/fail, and not AIAG GRR. (calculation_version 1.0.1)\n\nSemantic capability: `engineering.msa.hysteresis`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Maximum paired |y_up − y_down| — not a %Hysteresis / process-variation verdict\n\nLimitation: Not OLS of ε versus xref (Linearity) and not a single-shot measurement error\n\nLimitation: Does not take T and does not issue pass/fail\n\nLimitation: n≥2 index-paired points; not AIAG GRR", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.hysteresis.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "y_up": [ 0, 2, 4 ], "y_down": [ 0, 1, 4 ] }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.hysteresis.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gauge-rr": { "post": { "operationId": "calculate_engineering_msa_gauge_rr", "summary": "Gauge R&R", "description": "AIAG Gauge R&R compose: GRR=√(EV²+AV²), TV=√(GRR²+PV²), %GRR, ndc. Optional range-method EV=R̄/d2. Not a full ANOVA study. (calculation_version 1.0.0)\n\nSemantic capability: `engineering.msa.gauge_rr`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: AIAG compose of stated EV, AV, PV — not a full ANOVA Gauge R&R\n\nLimitation: Range-method EV uses d2 default 1.128 (n=2)\n\nLimitation: GRR must be > 0 for ndc", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.gauge_rr.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "ev": 3, "av": 4, "pv": 12 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.msa.gauge_rr.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/monte-carlo-tolerance": { "post": { "operationId": "calculate_engineering_tolerance_monte_carlo", "summary": "1-D Tolerance Analysis Workspace", "description": "1-D Tolerance Analysis Workspace — dimensional Monte Carlo with asymmetric ±tol, correlations (normal or NORTA), Spearman/Pearson/Sobol/Shapley sensitivity, σ convergence, LSL/USL yield, simulated capability, fingerprint, and snapshots. (calculation_version 1.12.0)\n\nSemantic capability: `engineering.tolerance.monte_carlo`.\n\nCalculation version: `1.12.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: 1-D stack; correlations use joint normal (all-normal) or Gaussian-copula NORTA (non-normal marginals)\n\nLimitation: Asymmetric normal uses two-piece scaling; uniform/triangular use [-tol_minus,+tol_plus]\n\nLimitation: Cp/Cpk/Ppk are simulated design-stage indices from overall MC mean/σ — not measured in-control SPC\n\nLimitation: Sobol requires independent inputs; for this linear stack Si=STi=analytic variance shares\n\nLimitation: Shapley variance attribution supports correlation; exact for d≤12, permutation estimate for d>12\n\nLimitation: Under NORTA, analytic σ uses Cov≈ρ·σi·σj (latent ρ); prefer Monte Carlo σ\n\nLimitation: Shared query must encode noms/sense; legacy tol1/tol2 alone is error-only (nominals 0)\n\nLimitation: Not full GD&T / 3-D geometry\n\nLimitation: MCP/agent input schema is canonical (no legacy field aliases); REST still accepts aliases\n\nLimitation: calculation_fingerprint is SHA-256; calculation_short_id is FNV-1a32 for UI only\n\nLimitation: MCP execute/inspect default detail_level=summary; pass full for histogram/Sobol/Shapley/contributors\n\nLimitation: Agent correlations use named pairs {a,b,rho} only (no i/j indexes)\n\nLimitation: Agent tolerances: half_tolerance OR both tol_plus+tol_minus (no single-sided agent form)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.12.0" ] }, "description": "Pin calculation_version (published: 1.12.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/engineering.tolerance.monte_carlo.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.12.0", "examples": [ "1.12.0" ] } } }, "example": { "inputs": { "tolerances": [ { "name": "A", "nominal": 10, "tol_plus": 0.1, "tol_minus": 0.05, "coefficient": 1, "distribution": "normal" }, { "name": "B", "nominal": 5, "half_tolerance": 0.2, "coefficient": -1, "distribution": "normal" } ], "sensitivity_method": "spearman", "LSL": 4.8, "USL": 5.2, "unit": "mm", "N": 20000, "seed": 42, "k_sigma": 3 }, "calculation_version": "1.12.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/engineering.tolerance.monte_carlo.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/opamp-noise": { "post": { "operationId": "calculate_electrical_opamp_noise", "summary": "Op-amp Noise", "description": "Flat-band op-amp output noise from en, gain, and bandwidth. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.opamp.noise`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Flat-band only; no 1/f", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.opamp.noise.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.opamp.noise.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/heatsink-rth": { "post": { "operationId": "calculate_electrical_thermal_heatsink_rth", "summary": "Heatsink Thermal Resistance", "description": "Junction temperature from effective θJA or θJC+θCS+θSA, or required heatsink θSA,max = (Tj,max−Ta)/P − θJC − θCS. (calculation_version 1.1.0)\n\nSemantic capability: `electrical.thermal.heatsink_rth`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Steady-state lumped Rθ only; not Zth(t) or CFD\n\nLimitation: θJA and θJC+θCS+θSA are exclusive models — mixing them is CONFLICTING_INPUTS\n\nLimitation: Required mode reports θSA,max, not total θJA\n\nLimitation: θCA / Rth_HS are rejected: θCA already includes the ambient-side path\n\nLimitation: Parallel PCB/package heat-flow paths are ignored on the explicit stack\n\nLimitation: P is device dissipation converted to heat, not load or output power\n\nLimitation: θSA,max ≤ 0 returns HEATSINK_INFEASIBLE and is not a purchasable heatsink", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.thermal.heatsink_rth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.thermal.heatsink_rth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pcb-trace-thermal": { "post": { "operationId": "calculate_electrical_pcb_trace_thermal", "summary": "PCB Trace Thermal", "description": "Copper trace I²R power and temperature rise with board Rth. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.pcb.trace_thermal`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Uniform copper; lumped board Rth", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.trace_thermal.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.pcb.trace_thermal.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/rectifier-ripple-cap": { "post": { "operationId": "calculate_electrical_rectifier_ripple_cap", "summary": "Rectifier Ripple Capacitor", "description": "Filter C or Vripple for half/full-wave capacitor-input rectifiers. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rectifier.ripple_cap`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant load current; ideal diodes", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rectifier.ripple_cap.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rectifier.ripple_cap.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/coulomb": { "post": { "operationId": "calculate_physics_em_coulomb", "summary": "Coulomb's Law", "description": "Electrostatic force F = k·|q1·q2|/r² between point charges. (calculation_version 1.0.0)\n\nSemantic capability: `physics.em.coulomb`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Point charges; εr=1", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.em.coulomb.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.em.coulomb.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/logic-gate": { "post": { "operationId": "calculate_electrical_digital_logic_gate", "summary": "Logic Gate", "description": "Basic Boolean gate outputs from binary inputs. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.digital.logic_gate`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Combinational Boolean only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.digital.logic_gate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.digital.logic_gate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/battery-aging": { "post": { "operationId": "calculate_electrical_battery_aging", "summary": "Linear Battery Aging", "description": "Linear capacity fade from independent cycle and calendar aging. Default k_cycle=0.0002/cycle and k_cal=0.02/year are illustrative. (calculation_version 1.0.2)\n\nSemantic capability: `electrical.battery.aging`.\n\nCalculation version: `1.0.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Linear independent cycle+calendar fade — not temperature, SOC, DoD, C-rate, or chemistry aware\n\nLimitation: Default k_cycle=0.0002/cycle and k_cal=0.02/year are illustrative\n\nLimitation: fade_frac is unclamped exposure and may exceed 1; SOH and capacity_Ah are clamped at 0", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.2" ] }, "description": "Pin calculation_version (published: 1.0.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery.aging.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.2", "examples": [ "1.0.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.battery.aging.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/buck-ripple": { "post": { "operationId": "calculate_electrical_buck_ripple", "summary": "Buck Converter Ripple", "description": "Assumed-CCM buck peak-to-peak inductor ripple ΔI_L,pp and optional capacitor-only ΔV_C,pp (ESR=0). (calculation_version 1.1.0)\n\nSemantic capability: `electrical.buck.ripple`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal CCM is assumed, not measured — no Iout, so CCM/DCM is not certified\n\nLimitation: ΔI_L_A and ΔV_out_V are peak-to-peak, not RMS or amplitude\n\nLimitation: ΔV_out_V is capacitor-only (ESR=0); ESR and switching transients are neglected\n\nLimitation: DCM, current-mode control dynamics, and non-ideal switch/diode drops are out of scope", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.buck.ripple.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.buck.ripple.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/celsius-kelvin": { "post": { "operationId": "calculate_units_temperature_celsius_kelvin", "summary": "Celsius ↔ Kelvin", "description": "Affine °C↔K with absolute-zero guards. (calculation_version 1.0.2)\n\nSemantic capability: `units.temperature.celsius_kelvin`.\n\nCalculation version: `1.0.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not Fahrenheit/Rankine", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.2" ] }, "description": "Pin calculation_version (published: 1.0.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.temperature.celsius_kelvin.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.2", "examples": [ "1.0.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.temperature.celsius_kelvin.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/psi-bar": { "post": { "operationId": "calculate_units_pressure_psi_bar", "summary": "PSI ↔ Bar", "description": "Positive pressure conversion using the international pound-force and inch. 1 bar ≈ 14.503773773020923 psi. (calculation_version 1.0.2)\n\nSemantic capability: `units.pressure.psi_bar`.\n\nCalculation version: `1.0.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Magnitude only; not gauge→absolute", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.2" ] }, "description": "Pin calculation_version (published: 1.0.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.pressure.psi_bar.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.2", "examples": [ "1.0.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.pressure.psi_bar.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mosfet-vth": { "post": { "operationId": "calculate_electrical_mosfet_vth", "summary": "MOSFET Threshold / Overdrive", "description": "Overdrive, square-law Id (cutoff / linear / saturation), or solve model Vth, with optional linear Vth(Tj). Vth is the long-channel square-law parameter, not datasheet VGS(th). (calculation_version 1.3.1)\n\nSemantic capability: `electrical.mosfet.vth`.\n\nCalculation version: `1.3.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Long-channel square-law only — not BSIM, velocity saturation, or short-channel\n\nLimitation: Vth is the model threshold parameter, not datasheet VGS(th) and not recommended gate drive\n\nLimitation: kn = μn·Cox·W/L such that Id_sat = ½·kn·Vod²; the ½ is not included in kn\n\nLimitation: Without Vds, Id uses the saturation equation; with Vds, region is cutoff / linear / saturation\n\nLimitation: Cutoff returns Id = 0 A; subthreshold leakage is not modeled\n\nLimitation: Linear Vth(Tj) does not scale kn / μ(T); default α = −0.002 V/°C is a Si planning value, not datasheet TCV", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.1" ] }, "description": "Pin calculation_version (published: 1.3.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.vth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.1", "examples": [ "1.3.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.mosfet.vth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ideal-gas": { "post": { "operationId": "calculate_physics_thermo_ideal_gas", "summary": "Ideal Gas Law", "description": "PV=nRT solve for P|V|n|T in SI units. (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.ideal_gas`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal gas; SI R default", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.ideal_gas.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.ideal_gas.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/heat-transfer": { "post": { "operationId": "calculate_physics_thermo_heat_transfer", "summary": "Heat Transfer", "description": "1-D conduction or convection heat rate. (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.heat_transfer`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: No radiation / CFD", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.heat_transfer.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.heat_transfer.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/receiver-sensitivity": { "post": { "operationId": "calculate_electrical_rf_receiver_sensitivity", "summary": "Receiver Sensitivity", "description": "MDS from NF, BW, and SNR_min at T0=290 K. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rf.receiver_sensitivity`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Flat NF; kT0=−174 dBm/Hz", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.receiver_sensitivity.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.receiver_sensitivity.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ldo-thermal": { "post": { "operationId": "calculate_electrical_ldo_thermal", "summary": "LDO Thermal", "description": "LDO dissipation and junction temperature from Rth. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.ldo.thermal`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Steady-state lumped Rth", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.ldo.thermal.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.ldo.thermal.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hz-rads": { "post": { "operationId": "calculate_units_frequency_hz_rads", "summary": "Hz ↔ rad/s", "description": "Angular frequency ω = 2πf with positive-frequency guards. (calculation_version 1.0.0)\n\nSemantic capability: `units.frequency.hz_rads`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not deg/s or rpm", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.frequency.hz_rads.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.frequency.hz_rads.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/tesla-gauss": { "post": { "operationId": "calculate_units_magnetic_tesla_gauss", "summary": "Tesla ↔ Gauss", "description": "Magnetic flux density with 1 T = 10000 G. (calculation_version 1.0.0)\n\nSemantic capability: `units.magnetic.tesla_gauss`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Non-negative B only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.magnetic.tesla_gauss.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.magnetic.tesla_gauss.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/wavelength": { "post": { "operationId": "calculate_electrical_rf_wavelength", "summary": "Wavelength", "description": "λ = c·VF/f in vacuum or dielectric (VF or εr). (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rf.wavelength`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Mode lambda needs f_Hz; mode freq needs lambda_m\n\nLimitation: Non-dispersive VF; no waveguide cutoff", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.wavelength.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.wavelength.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/coax-impedance": { "post": { "operationId": "calculate_electrical_rf_coax", "summary": "Coax Impedance", "description": "Z0 of coaxial line from shield inner diameter D, center-conductor diameter d, and εr. Omitted εr defaults to 1.0. (calculation_version 1.0.1)\n\nSemantic capability: `electrical.rf.coax`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Does not model conductor loss\n\nLimitation: Does not model dielectric loss / tanδ\n\nLimitation: Does not model dispersion\n\nLimitation: Does not model connectors or discontinuities\n\nLimitation: Does not model higher-order modes", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.coax.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.coax.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/lc-match": { "post": { "operationId": "calculate_electrical_rf_lc_match", "summary": "L-section LC Match", "description": "Narrowband real RL→Z0 L-section dual solutions. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rf.lc_match`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real ZL only; narrowband; no stub match", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.lc_match.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.lc_match.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/smith-chart": { "post": { "operationId": "calculate_electrical_rf_smith", "summary": "Smith Chart (Impedance Matching)", "description": "RF Smith Chart & Matching Workspace: mode-discriminated Agent API, strict match-steps, Touchstone S11, auto-match, SVG overlays. (calculation_version 1.6.3)\n\nSemantic capability: `electrical.rf.smith`.\n\nCalculation version: `1.6.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: No multi-section Chebyshev / broadband optimizer\n\nLimitation: Full bilateral gain redesign with S12 feedback not supported\n\nLimitation: Drag-to-tune and S21/stability overlays are UI-side (API returns numerical modes)\n\nLimitation: Noise circles require Touchstone noise params (NFmin, Γopt, Rn); not inferred from S alone\n\nLimitation: Passive Z↔Γ / matching: R≥0 and |Γ|≤1; active overlay circles may extend outside the unit circle", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.6.3" ] }, "description": "Pin calculation_version (published: 1.6.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.smith.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.6.3", "examples": [ "1.6.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.6.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.smith.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gamma-z": { "post": { "operationId": "calculate_electrical_rf_gamma_z", "summary": "Γ ↔ Z (Complex)", "description": "Complex reflection coefficient ↔ normalized impedance with VSWR/RL. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.rf.gamma_z`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Normalized z; |Γ|≤1 for passive", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.gamma_z.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.rf.gamma_z.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kwh-joule": { "post": { "operationId": "calculate_units_energy_kwh_joule", "summary": "kWh ↔ Joule", "description": "Energy conversion with 1 kWh = 3.6 MJ. (calculation_version 1.0.0)\n\nSemantic capability: `units.energy.kwh_joule`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact SI factor 3.6e6 only", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.energy.kwh_joule.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.energy.kwh_joule.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/watt-hp": { "post": { "operationId": "calculate_units_power_watt_hp", "summary": "Watt ↔ Horsepower", "description": "Mechanical horsepower: 1 hp = 745.6998715822702 W. (calculation_version 1.0.0)\n\nSemantic capability: `units.power.watt_hp`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Mechanical hp only (not metric PS)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.power.watt_hp.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.power.watt_hp.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/projectile": { "post": { "operationId": "calculate_physics_kinematics_projectile", "summary": "Projectile Motion", "description": "Flat-ground projectile range, apex, and flight time (no drag). (calculation_version 1.0.0)\n\nSemantic capability: `physics.kinematics.projectile`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: No drag; flat ground; angle in (0,90)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.projectile.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.projectile.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/force": { "post": { "operationId": "calculate_physics_dynamics_force", "summary": "Force (F=ma)", "description": "Newton second law solve for F, a, or m. (calculation_version 1.0.0)\n\nSemantic capability: `physics.dynamics.force`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Point-mass Newtonian; no relativity", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.force.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.force.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/reynolds": { "post": { "operationId": "calculate_physics_fluid_reynolds", "summary": "Reynolds Number", "description": "Re = ρvL/μ with laminar/turbulent pipe guidance bands. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.reynolds`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Pipe guidance bands 2300/4000; not a stability proof", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.reynolds.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.reynolds.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/colebrook": { "post": { "operationId": "calculate_physics_fluid_colebrook", "summary": "Colebrook Friction Factor", "description": "Colebrook–White Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Not laminar 64/Re. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.colebrook`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Turbulent pipes Re ≥ 4000 — not laminar f=64/Re\n\nLimitation: Not a Moody-chart lookup\n\nLimitation: Does not compose Darcy–Weisbach head loss", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.colebrook.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Re": 100000, "rel_roughness": 0.0002 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.colebrook.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/darcy-weisbach": { "post": { "operationId": "calculate_physics_fluid_darcy_weisbach", "summary": "Darcy–Weisbach", "description": "Pipe head loss hf = f L v²/(2 g D) and Δp = ρ g hf from a given Darcy friction factor. Does not solve Colebrook for f. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.darcy_weisbach`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Incompressible; constant Darcy friction factor; circular pipe\n\nLimitation: Does not solve Colebrook for f\n\nLimitation: Not Hazen–Williams, not minor-loss K v²/2g\n\nLimitation: Not volumetric flow Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.darcy_weisbach.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "f": 0.02, "L": 10, "v": 2, "D": 0.1, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.darcy_weisbach.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/manning-formula": { "post": { "operationId": "calculate_physics_fluid_manning", "summary": "Manning formula", "description": "SI Manning open-channel discharge Q = (1/n) A R^{2/3} S^{1/2}. k=1. Not Q=Av, not Darcy–Weisbach, not a weir, not US customary 1.486. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.manning`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: SI only: k=1. US customary 1.486 is out of scope\n\nLimitation: Uniform open-channel flow; R=A/P\n\nLimitation: Not Q=Av identities (see /calc/physics/flow-rate)\n\nLimitation: Not Darcy–Weisbach pipe head loss\n\nLimitation: Not a weir or orifice", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.manning.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "mode": "discharge", "n": 0.013, "A": 1, "R": 0.5, "S": 0.001 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.manning.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/weir-discharge": { "post": { "operationId": "calculate_physics_fluid_weir", "summary": "Weir discharge", "description": "Thin-plate weir discharge. Rectangular Q=(2/3) C_d L √(2g) H^{3/2}. Triangular Q=(8/15) C_d √(2g) tan(θ/2) H^{5/2}. Not Manning, not Q=Av, not Darcy, not an orifice, not Francis contractions. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.weir`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Thin-plate weir; free nappe; SI g=9.80665 unless given\n\nLimitation: Rectangular: Q=(2/3) C_d L √(2g) H^{3/2}; not Francis contractions\n\nLimitation: Triangular: Q=(8/15) C_d √(2g) tan(θ/2) H^{5/2}\n\nLimitation: Not Manning, not Q=Av, not Darcy, not an orifice", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.weir.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "mode": "rectangular", "L": 1, "H": 0.2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.weir.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/orifice-discharge": { "post": { "operationId": "calculate_physics_fluid_orifice", "summary": "Orifice discharge", "description": "Sharp-edged orifice. Tank Q=C_d A √(2gH). Meter Q=C_d E A_t √(2Δp/ρ) with E=1/√(1−β⁴). Not a weir, not Q=Av, not Darcy, not Manning, not compressible ISO ε. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.orifice`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Sharp-edged orifice; SI; default C_d=0.61\n\nLimitation: Tank: Q=C_d A √(2gH); not a weir H^{3/2}\n\nLimitation: Meter: Q=C_d E A_t √(2Δp/ρ); incompressible; user C_d; not ISO ε(Re)\n\nLimitation: Not weir, not Q=Av, not Darcy, not Manning", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.orifice.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "mode": "tank", "d": 0.05, "H": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.orifice.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pump-power": { "post": { "operationId": "calculate_physics_fluid_pump", "summary": "Pump power", "description": "Pump hydraulic and shaft power P_h=ρgQH, P=P_h/η, plus affinity Q∝ND, H∝N²D², P∝N³D³. Not an orifice, not a weir, not Q=Av, not Darcy, not NPSH. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pump`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Incompressible pump; P_h = ρ g Q H; P = P_h/η; default ρ=1000 kg/m³; η in (0, 1]\n\nLimitation: Affinity: Q∝N D, H∝N² D², P∝N³ D³; geometrically similar; same fluid\n\nLimitation: Not orifice, not weir, not Q=Av, not Darcy, not NPSH, not a catalog curve", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pump.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "mode": "power", "Q": 0.05, "H": 20, "eta": 0.75 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pump.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/npsh": { "post": { "operationId": "calculate_physics_fluid_npsh", "summary": "Net positive suction head", "description": "NPSH available: open tank (p_atm−p_v)/ρg + z − hf, or suction flange (p_s−p_v)/ρg + v_s²/2g + z_s. Optional NPSHr margin. Not pump power, not orifice, not weir, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.npsh`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: NPSHa = (p_s − p_v)/(ρ g) + v_s²/(2g) + z_s; pressures absolute; SI\n\nLimitation: Open tank: p_s=p_atm (default 101325 Pa), z_s=z−hf, v_s=0; hf is an input\n\nLimitation: Not pump power, not orifice, not weir, not Q=Av, not Darcy, not a catalog NPSHr curve, not steam p_v(T)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.npsh.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "p_v": 2339, "z": 2, "hf": 0.5 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.npsh.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hydraulic-diameter": { "post": { "operationId": "calculate_physics_fluid_hydraulic_diameter", "summary": "Hydraulic diameter", "description": "Hydraulic diameter D_h=4A/P_w. Full circular pipe D_h=D, closed rectangular duct 2ab/(a+b), annulus D_o−D_i. Not Q=Av, not Manning Q, not Reynolds, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.hydraulic_diameter`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: D_h = 4 A / P_w; R = A / P_w = D_h / 4\n\nLimitation: Full circular pipe: D_h = D; closed rectangular duct: D_h = 2ab/(a+b); annulus: D_h = D_o − D_i\n\nLimitation: Not Q=Av, not Manning Q, not Reynolds, not Darcy, not a weir or orifice", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.hydraulic_diameter.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "A": 0.01, "Pw": 0.4 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.hydraulic_diameter.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hazen-williams": { "post": { "operationId": "calculate_physics_fluid_hazen_williams", "summary": "Hazen–Williams", "description": "SI Hazen–Williams circular water-pipe head loss hf=10.67 L Q^{1.852}/(C^{1.852} D^{4.87}). Invert Q, D, or C. Not Darcy, not Colebrook, not Manning, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.hazen_williams`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: SI Hazen–Williams: hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87})\n\nLimitation: Circular full-flow water pipe; empirical C; k=10.67; not US gpm/in\n\nLimitation: Not Darcy–Weisbach, not Colebrook, not Manning, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.hazen_williams.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "C": 120, "L": 100, "Q": 0.02, "D": 0.2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.hazen_williams.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/minor-loss": { "post": { "operationId": "calculate_physics_fluid_minor_loss", "summary": "Minor loss", "description": "Fitting minor loss h_m=K v²/(2g). Optional Δp=ρ g h_m. Invert K or v. Not Darcy, not Hazen–Williams, not orifice, not Q=Av, not equivalent length. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.minor_loss`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Minor loss h_m = K v² / (2g); optional Δp = ρ g h_m\n\nLimitation: K is an empirical fitting coefficient; not Darcy f, not equivalent length\n\nLimitation: Not Darcy–Weisbach, not Hazen–Williams, not orifice, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.minor_loss.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "K": 0.5, "v": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.minor_loss.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/venturi": { "post": { "operationId": "calculate_physics_fluid_venturi", "summary": "Venturi meter", "description": "Incompressible venturi Q=C_d A2 √(2Δp/(ρ(1−β⁴))), β=D2/D1. Default C_d=0.98. Optional same-fluid Δh. Not an orifice wrap, not Q=Av, not Darcy, not Cv/Kv. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.venturi`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Incompressible venturi: Q = C_d A2 √(2Δp/(ρ(1−β⁴))), β=D2/D1; default C_d=0.98\n\nLimitation: Ideal Bernoulli Q_ideal uses C_d=1; optional same-fluid manometer Δh, Δp=ρ g Δh\n\nLimitation: Not an orifice plate, not Q=Av, not Darcy, not minor-loss K, not valve Cv/Kv", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.venturi.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D1": 0.1, "D2": 0.05, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.venturi.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/valve-flow-coefficient": { "post": { "operationId": "calculate_physics_fluid_valve_cv", "summary": "Valve flow coefficient", "description": "Incompressible liquid valve Q_m³/h=Kv √(Δp_bar/SG). Kv=0.865 Cv (IEC 60534-1). SI Q in m³/s, Δp in Pa. Not a venturi wrap, not orifice, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.valve_cv`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Incompressible liquid valve: Q_m³/h = Kv √(Δp_bar/SG); Kv = 0.865 Cv (IEC 60534-1)\n\nLimitation: SI Q in m³/s, Δp in Pa; default SG=1 (water); not gas, not choked\n\nLimitation: Not a venturi, not an orifice, not Q=Av, not Darcy, not minor-loss K", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.valve_cv.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Kv": 10, "dP": 100000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.valve_cv.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/chezy-formula": { "post": { "operationId": "calculate_physics_fluid_chezy", "summary": "Chezy formula", "description": "Open-channel Chezy V=C √(R S). C is Chezy C, not Manning n, not Hazen–Williams pipe C. Not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.chezy`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Open-channel Chezy: V = C √(R S); C is Chezy C, not Manning n, not Hazen–Williams C\n\nLimitation: Uniform flow; R is hydraulic radius; S is friction slope\n\nLimitation: Not Manning, not Q=Av, not Darcy, not Hazen–Williams, not a weir", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.chezy.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "C": 50, "R": 1, "S": 0.001 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.chezy.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pitot-tube": { "post": { "operationId": "calculate_physics_fluid_pitot", "summary": "Pitot tube", "description": "Incompressible pitot-static v=C √(2Δp/ρ). Default C=1. Not a venturi wrap, not orifice, not Q=Av, not two-station Bernoulli. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pitot`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Incompressible pitot-static: v = C √(2 Δp / ρ); default C=1\n\nLimitation: Δp is dynamic pressure P0 − P_static; C is a probe coefficient, not orifice C_d\n\nLimitation: Not a venturi, not an orifice, not Q=Av, not two-station Bernoulli", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pitot.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "dP": 5000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pitot.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/froude-number": { "post": { "operationId": "calculate_physics_fluid_froude", "summary": "Froude number", "description": "Open-channel Fr=v/√(gL). Default g=9.80665. Not Reynolds, not Manning, not Chezy, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.froude`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Froude Fr = v / √(g L); default g=9.80665 m/s²\n\nLimitation: Free-surface: Fr<1 subcritical, Fr=1 critical, Fr>1 supercritical\n\nLimitation: Not Reynolds, not Manning, not Chezy, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.froude.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v": 1, "L": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.froude.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/weber-number": { "post": { "operationId": "calculate_physics_fluid_weber", "summary": "Weber number", "description": "We=ρv²L/σ. Not Reynolds, not Froude, not Manning, not Q=Av, not capillary Ca=μv/σ. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.weber`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Weber We = ρ v² L / σ\n\nLimitation: Inertia vs surface tension; σ is interfacial tension, not viscosity μ\n\nLimitation: Not Reynolds, not Froude, not Manning, not Q=Av, not capillary Ca=μv/σ", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.weber.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "rho": 1000, "v": 1, "L": 0.072, "sigma": 0.072 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.weber.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hydraulic-jump": { "post": { "operationId": "calculate_physics_fluid_hydraulic_jump", "summary": "Hydraulic jump", "description": "Rectangular sequent depths y2/y1=(√(1+8Fr₁²)−1)/2. Fr₁>1. Not a Froude wrap, not Manning, not a weir, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.hydraulic_jump`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Rectangular hydraulic jump: y2/y1 = (√(1+8 Fr₁²) − 1)/2; Fr₁ > 1\n\nLimitation: ΔE = (y2 − y1)³ / (4 y1 y2); Fr₂ = Fr₁ / (y2/y1)^{3/2}\n\nLimitation: Not a Froude wrap, not Manning, not Chezy, not a weir, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.hydraulic_jump.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "y1": 1, "Fr": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.hydraulic_jump.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hagen-poiseuille": { "post": { "operationId": "calculate_physics_fluid_poiseuille", "summary": "Hagen–Poiseuille", "description": "Laminar circular-pipe Q=πΔpD⁴/(128μL). Not Darcy f, not Colebrook, not Q=Av, not Manning. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.poiseuille`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Laminar Hagen–Poiseuille: Q = π Δp D⁴ / (128 μ L); circular, fully developed, Newtonian\n\nLimitation: Mean speed v = 4Q/(π D²) is reported, not an input\n\nLimitation: Not Darcy f, not Colebrook, not Q=Av, not Manning", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.poiseuille.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "dP": 1000, "D": 0.002, "L": 1, "mu": 0.001 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.poiseuille.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/specific-energy": { "post": { "operationId": "calculate_physics_fluid_specific_energy", "summary": "Specific energy", "description": "Open-channel E=y+v²/(2g). Not a Froude wrap, not a hydraulic jump, not Manning, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.specific_energy`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Open-channel specific energy: E = y + v² / (2g); default g=9.80665 m/s²\n\nLimitation: Invert y = E − v²/(2g) and v = √(2g(E−y)); require E > y\n\nLimitation: Not a Froude wrap, not a hydraulic jump, not Manning, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.specific_energy.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "y": 1, "v": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.specific_energy.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/critical-depth": { "post": { "operationId": "calculate_physics_fluid_critical_depth", "summary": "Critical depth", "description": "Rectangular yc=(q²/g)^{1/3}. Not a Froude wrap, not specific energy, not a hydraulic jump, not Manning, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.critical_depth`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Rectangular critical depth: yc = (q²/g)^{1/3}; q = Q/b; default g=9.80665 m/s²\n\nLimitation: Critical speed vc = √(g yc) is reported, not an input; Fr=1 is the definition, not a Froude wrap\n\nLimitation: Not a Froude wrap, not specific energy E, not a hydraulic jump, not Manning, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.critical_depth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "q": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.critical_depth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/water-hammer": { "post": { "operationId": "calculate_physics_fluid_water_hammer", "summary": "Water hammer", "description": "Joukowsky Δp=ρcΔv. Not Darcy f, not minor-loss K, not Moens–Korteweg, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.water_hammer`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Joukowsky water hammer: Δp = ρ c Δv; h = Δp/(ρ g); default ρ=1000 kg/m³; default g=9.80665 m/s²\n\nLimitation: c is the given celerity, not Moens–Korteweg from bulk modulus K, D, e, E\n\nLimitation: Not Darcy f, not Colebrook, not minor-loss K, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.water_hammer.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "c": 1000, "dV": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.water_hammer.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/wave-celerity": { "post": { "operationId": "calculate_physics_fluid_wave_celerity", "summary": "Wave celerity", "description": "Korteweg–Hall c=√[(K/ρ)/(1+(K D)/(E e))]. Not Joukowsky Δp, not Darcy f, not minor-loss K, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.wave_celerity`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Korteweg–Hall wave celerity: c = √[(K/ρ)/(1+(K D)/(E e))]; default ρ=1000 kg/m³; thin wall; ψ=1\n\nLimitation: K is fluid bulk modulus, E is wall Young’s modulus; not Joukowsky Δp=ρcΔv\n\nLimitation: Not Darcy f, not minor-loss K, not Q=Av, not Y=(F/A)/(ΔL/L0)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.wave_celerity.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "K": 2200000000, "D": 1, "e": 0.01, "E": 200000000000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.wave_celerity.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pipe-period": { "post": { "operationId": "calculate_physics_fluid_pipe_period", "summary": "Pipe period", "description": "T=2L/c. Not Joukowsky Δp, not Korteweg–Hall c from K/D/e/E, not Darcy f, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pipe_period`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Pipe period T = 2L/c; c is a given celerity, not Korteweg–Hall from K, D, e, E\n\nLimitation: Sudden-closure Joukowsky applies when valve time t < T; this page computes T, not Δp\n\nLimitation: Not Joukowsky Δp=ρcΔv, not Darcy f, not minor-loss K, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_period.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "L": 1000, "c": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_period.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cavitation-number": { "post": { "operationId": "calculate_physics_fluid_cavitation", "summary": "Cavitation number", "description": "σ=(p−p_v)/(½ρv²). Not NPSH, not Thoma NPSH/H, not Weber, not Euler Eu=Δp/(ρv²). (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.cavitation`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cavitation number σ = (p − p_v) / (½ ρ v²); default ρ=1000 kg/m³; p and p_v absolute Pa\n\nLimitation: Not NPSH head, not Thoma σ_Th=NPSH/H, not Weber We=ρv²L/σ, not Euler Eu=Δp/(ρ v²)\n\nLimitation: Not Reynolds, not capillary Ca=μv/σ, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.cavitation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "p": 150000, "p_v": 50000, "v": 10 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.cavitation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sudden-expansion": { "post": { "operationId": "calculate_physics_fluid_sudden_expansion", "summary": "Sudden expansion", "description": "Borda–Carnot h=(v1−v2)²/(2g). Not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.sudden_expansion`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Borda–Carnot sudden expansion: h = (v1 − v2)² / (2g); K = (1 − v2/v1)² is reported, not an input\n\nLimitation: Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ (v1−v2)² / 2; incompressible; A2 > A1\n\nLimitation: Not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av, not sudden contraction", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.sudden_expansion.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v1": 2, "v2": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.sudden_expansion.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sudden-contraction": { "post": { "operationId": "calculate_physics_fluid_sudden_contraction", "summary": "Sudden contraction", "description": "Vena-contracta h=(1/C_c−1)² v2²/(2g). Default C_c=0.62. Not expansion (v1−v2)², not minor-loss K given, not orifice C_d, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.sudden_contraction`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Vena-contracta sudden contraction: h = (1/C_c − 1)² v2² / (2g); default C_c=0.62; K is reported, not an input\n\nLimitation: Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ K v2² / 2; incompressible; C_c in (0, 1)\n\nLimitation: Not sudden expansion (v1−v2)², not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.sudden_contraction.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v2": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.sudden_contraction.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gradual-expansion": { "post": { "operationId": "calculate_physics_fluid_gradual_expansion", "summary": "Gradual expansion", "description": "Conical diffuser h=k(v1−v2)²/(2g), k=2.6 sin(α). Not sudden expansion, not minor-loss K given, not orifice C_d, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.gradual_expansion`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Conical diffuser: h = k (v1 − v2)² / (2g); k = 2.6 sin(α); α is wall half-angle; k and K are reported, not inputs\n\nLimitation: Require 0 < α < arcsin(1/2.6); k=1 is sudden expansion, not this page; default g=9.80665; default ρ=1000 for Δp\n\nLimitation: Not sudden expansion, not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av, not sudden contraction", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.gradual_expansion.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v1": 2, "v2": 1, "alpha_deg": 7 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.gradual_expansion.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gradual-contraction": { "post": { "operationId": "calculate_physics_fluid_gradual_contraction", "summary": "Gradual contraction", "description": "Conical contraction h=K v2²/(2g), K=0.5 sin(α)(1−v1/v2). Not sudden contraction, not gradual expansion, not minor-loss K given, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.gradual_contraction`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Conical contraction: h = K v2² / (2g); K = 0.5 sin(α) (1 − v1/v2); α is wall half-angle; k and K are reported, not inputs\n\nLimitation: Require 0 < α < 90°; α=90° is sudden contraction, not this page; default g=9.80665; default ρ=1000 for Δp; v2 > v1\n\nLimitation: Not sudden contraction (C_c), not gradual expansion (v1−v2)², not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.gradual_contraction.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v1": 1, "v2": 2, "alpha_deg": 7 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.gradual_contraction.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pipe-bend": { "post": { "operationId": "calculate_physics_fluid_pipe_bend", "summary": "Pipe bend", "description": "Circular-arc bend h=K v²/(2g), K=0.21 (θ/90)/√(R/D). Not minor-loss K given, not mitered, not Darcy, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pipe_bend`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Circular-arc bend: h = K v² / (2g); K = 0.21 (θ/90)/√(R/D); Idelchik 90° B1 scaled linearly in θ; K is reported, not an input\n\nLimitation: Require 0 < θ ≤ 180° and R/D ≥ 1; default g=9.80665; default ρ=1000 for Δp; incompressible\n\nLimitation: Not minor-loss K given, not mitered R/D<1, not Darcy f, not orifice C_d, not Q=Av, not gradual contraction α", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_bend.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2, "theta_deg": 90, "rd": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_bend.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mitered-bend": { "post": { "operationId": "calculate_physics_fluid_mitered_bend", "summary": "Mitered bend", "description": "Sharp miter h=K v²/(2g), K=n [sin²(δ/2)+2 sin⁴(δ/2)], δ=θ/n. Not circular-arc R/D, not minor-loss K given, not Crane f_T, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.mitered_bend`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Sharp segmented miter: h = K v² / (2g); K = n [sin²(δ/2) + 2 sin⁴(δ/2)], δ = θ/n; K is reported, not an input\n\nLimitation: Require n ≥ 1 integer, 0 < θ ≤ 180°, and each miter δ ≤ 90° (n=1 therefore θ ≤ 90°); default g=9.80665; default ρ=1000 for Δp; incompressible\n\nLimitation: Not circular-arc R/D, not minor-loss K given, not Crane f_T, not Darcy f, not orifice C_d, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.mitered_bend.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2, "theta_deg": 90, "n_miters": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.mitered_bend.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pipe-entrance": { "post": { "operationId": "calculate_physics_fluid_pipe_entrance", "summary": "Pipe entrance", "description": "Geometric inlet h=K v²/(2g): flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]. Not catalog K, not circular-arc R/D, not mitered n, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pipe_entrance`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Geometric pipe inlet: h = K v² / (2g); flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]; K is reported, not an input\n\nLimitation: Require kind flush|reentrant|rounded; rounded needs 0 < rᵢ/D ≤ 1; default g=9.80665; default ρ=1000 for Δp; incompressible; from a large reservoir\n\nLimitation: Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not Darcy f, not orifice C_d, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_entrance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2, "kind": "flush" }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_entrance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pipe-exit": { "post": { "operationId": "calculate_physics_fluid_pipe_exit", "summary": "Pipe exit", "description": "Pipe into a large reservoir h=K v²/(2g) with K=1. Not catalog K, not pipe-entrance geometry, not sudden expansion (v1−v2)², not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pipe_exit`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Pipe exit into a large reservoir: h = K v² / (2g) with K=1; kinetic energy is dissipated; K is reported, not an input\n\nLimitation: Default g=9.80665; default ρ=1000 for Δp; incompressible; one mean speed in the pipe; exit geometry does not change K\n\nLimitation: Not catalog minor-loss K given, not pipe-entrance flush/reentrant/rounded, not sudden expansion (v1−v2)², not Darcy f, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_exit.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_exit.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pipe-tee": { "post": { "operationId": "calculate_physics_fluid_pipe_tee", "summary": "Pipe tee", "description": "Equal-area sharp 90° T h=K v_c²/(2g) from dividing/combining and branch/run split. Not catalog K, not circular-arc, not mitered, not entrance/exit, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pipe_tee`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Equal-area sharp 90° T: h = K v_c² / (2g); K referenced to common-channel speed; K is reported, not an input\n\nLimitation: Dividing: branch K=1+q², run K=0.4(1−q)². Combining: branch K=1+q², run K=1.55q−q². q=Q_path/Q_c in [0,1]; default g=9.80665; default ρ=1000 for Δp\n\nLimitation: Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not a non-90° wye, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_tee.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2, "kind": "dividing", "path": "branch", "q_ratio": 0.5 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_tee.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pipe-wye": { "post": { "operationId": "calculate_physics_fluid_pipe_wye", "summary": "Pipe wye", "description": "Equal-area sharp wye h=K v_c²/(2g) from α∈(0,90°), dividing/combining, and branch/run split. Not a 90° tee, not catalog K, not circular-arc, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pipe_wye`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Equal-area sharp wye: h = K v_c² / (2g); K referenced to common-channel speed; α ∈ (0, 90°); K is reported, not an input\n\nLimitation: Branch K=1+q²−2q cos α. Dividing run K=0.4(1−q)². Combining run K=1−q²−2q(1−q)cos α. q=Q_path/Q_c in [0,1]; default g=9.80665; default ρ=1000 for Δp\n\nLimitation: Not a 90° tee, not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_wye.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2, "kind": "dividing", "path": "branch", "q_ratio": 0.5, "alpha_deg": 45 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_wye.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pipe-cross": { "post": { "operationId": "calculate_physics_fluid_pipe_cross", "summary": "Pipe cross", "description": "Equal-area sharp 90° four-way h=K v_c²/(2g) from dividing/combining and branch/through split with equal opposite laterals. Not a 90° tee, not a wye, not catalog K, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.pipe_cross`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Equal-area sharp 90° four-way cross: h = K v_c² / (2g); K referenced to common-channel speed; two opposite laterals are equal; K is reported, not an input\n\nLimitation: Dividing: branch K=(1+q)², run K=0.4(1−q)². Combining: branch K=1+q²−4(1−2q)²/(2−q), run K=1+q²−q²/[1+q(0.75+0.25q)²]. Branch q≤0.5; default g=9.80665; default ρ=1000 for Δp\n\nLimitation: Not a 90° tee, not a non-90° wye, not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_cross.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2, "kind": "dividing", "path": "branch", "q_ratio": 0.5 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.pipe_cross.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/concentric-reducer": { "post": { "operationId": "calculate_physics_fluid_concentric_reducer", "summary": "Concentric reducer", "description": "Area-ratio reducer h=K v₂²/(2g) with K=0.5(1−A₂/A₁) referenced to downstream speed. Not sudden expansion, not gradual contraction α, not C_c, not catalog K, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.concentric_reducer`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Concentric reducer: h = K v₂² / (2g); K = 0.5 (1 − A₂/A₁); K referenced to downstream speed; K is reported, not an input\n\nLimitation: A₂/A₁ in (0, 1); default g=9.80665; default ρ=1000 for Δp; incompressible; geometry from area_ratio or A1+A2 or D1+D2\n\nLimitation: Not sudden expansion (v1−v2)², not gradual contraction α, not vena-contracta C_c, not catalog minor-loss K given, not a four-way cross, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.concentric_reducer.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "v_m_s": 2, "area_ratio": 0.5 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.concentric_reducer.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/iso-nozzle": { "post": { "operationId": "calculate_physics_fluid_iso_nozzle", "summary": "ISO 5167 nozzle", "description": "ISO 5167-3 ISA 1932 nozzle Q=C E A2 √(2Δp/ρ) with C from β and Re_D. Not a venturi wrap with C_d=0.98, not orifice C_d=0.61, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.iso_nozzle`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: ISO 5167-3 ISA 1932 nozzle: Q = C E A2 √(2Δp/ρ); C from β and Re_D; incompressible ε=1; C is reported, not an input\n\nLimitation: C = 0.9900 − 0.2262 β^4.1 − (0.00175 β² − 0.0033 β^4.15)(10^6/Re_D)^1.15; β∈[0.30,0.80]; Re_D∈[7e4,1e7]; D≥50 mm\n\nLimitation: Not a venturi wrap with given C_d=0.98, not orifice C_d=0.61, not Q=Av, not Darcy f, not compressible ε", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_nozzle.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D1": 0.1, "D2": 0.05, "Re_D": 1000000, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_nozzle.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/iso-orifice": { "post": { "operationId": "calculate_physics_fluid_iso_orifice", "summary": "ISO 5167 orifice plate", "description": "ISO 5167-2 orifice plate Q=C E A2 √(2Δp/ρ) with Reader–Harris/Gallagher C from β, Re_D, and tapping. Not tank orifice C_d A √(2gH), not given C_d=0.61, not ISA 1932, not venturi C_d=0.98, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.iso_orifice`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: ISO 5167-2 orifice plate: Q = C E A2 √(2Δp/ρ); Reader–Harris/Gallagher C from β, Re_D, and tapping; incompressible ε=1; C is reported, not an input\n\nLimitation: Corner tappings default (L1=L2′=0); flange L1=L2′=25.4 mm/D; β∈[0.10,0.75]; D∈[50 mm,1000 mm]; d≥12.5 mm; Re_D≥5000 (β≤0.56) or 16000 β² (β>0.56)\n\nLimitation: Not tank orifice C_d A √(2gH), not given C_d=0.61, not ISA 1932 nozzle, not venturi C_d=0.98, not Q=Av, not Darcy f, not D-D/2 tappings, not compressible ε", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_orifice.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D": 0.1, "d": 0.05, "Re_D": 1000000, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_orifice.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/iso-venturi": { "post": { "operationId": "calculate_physics_fluid_iso_venturi", "summary": "ISO 5167 Venturi tube", "description": "ISO 5167-4 classical Venturi tube Q=C E A2 √(2Δp/ρ) with C from convergent type. Not given C_d=0.98, not ISA 1932, not RHG orifice, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.iso_venturi`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: ISO 5167-4 classical Venturi tube: Q = C E A2 √(2Δp/ρ); C from convergent type; β and Re_D bound the ISO envelope; incompressible ε=1; C is reported, not an input\n\nLimitation: Machined C=0.995, D∈[50 mm,250 mm], β∈[0.40,0.75], Re_D∈[2e5,1e6]. Rough-welded C=0.985. As-cast C=0.984\n\nLimitation: Not a given C_d=0.98, not ISA 1932 nozzle, not RHG orifice, not Q=Av, not Darcy f, not compressible ε", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_venturi.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D1": 0.1, "D2": 0.05, "Re_D": 500000, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_venturi.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/long-radius-nozzle": { "post": { "operationId": "calculate_physics_fluid_long_radius_nozzle", "summary": "ISO 5167 long-radius nozzle", "description": "ISO 5167-3 long-radius nozzle Q=C E A2 √(2Δp/ρ) with C=0.9965−0.00653 β^{0.5}. Not ISA 1932, not given C_d=0.98, not RHG orifice, not ISO 5167-4 type C, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.long_radius_nozzle`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: ISO 5167-3 long-radius nozzle: Q = C E A2 √(2Δp/ρ); C = 0.9965 − 0.00653 β^{0.5}; incompressible ε=1; C is reported, not an input\n\nLimitation: C from β, not Re_D; Re_D∈[1e4,1e7] is the ISO envelope; β∈[0.20,0.80]; D∈[50 mm, 630 mm]\n\nLimitation: Not ISA 1932 C(β,Re), not given C_d=0.98, not RHG orifice, not ISO 5167-4 type C, not Q=Av, not Darcy f, not compressible ε", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.long_radius_nozzle.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D1": 0.1, "D2": 0.05, "Re_D": 1000000, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.long_radius_nozzle.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/iso-cone": { "post": { "operationId": "calculate_physics_fluid_iso_cone", "summary": "ISO 5167 cone meter", "description": "ISO 5167-5 uncalibrated cone Q=C E A √(2Δp/ρ) with C=0.82 and β=√(1−(d_c/D)²). Not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius, not given C_d, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.iso_cone`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: ISO 5167-5 uncalibrated cone: Q = C E A √(2Δp/ρ); C=0.82; β=√(1−(d_c/D)²); A=(π/4) D² β² annulus; incompressible ε=1; C is reported, not an input\n\nLimitation: Uncalibrated C=0.82; Re_D∈[8e4, 1.2e7] is the ISO envelope; β∈[0.45,0.75]; D∈[50 mm, 500 mm]; larger cone lowers β\n\nLimitation: Not ISA 1932 C(β,Re), not RHG orifice, not ISO 5167-4 type C, not long-radius C(β), not given C_d, not Q=Av, not Darcy f, not compressible ε", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_cone.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D": 0.1, "d_c": 0.08, "Re_D": 1000000, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_cone.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/iso-wedge": { "post": { "operationId": "calculate_physics_fluid_iso_wedge", "summary": "ISO 5167 wedge meter", "description": "ISO 5167-6 uncalibrated wedge Q=C E A √(2Δp/ρ) with C=0.77−0.09β and β from circular-segment h/D. Not cone C=0.82, not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius, not given C_d, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.iso_wedge`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: ISO 5167-6 uncalibrated wedge: Q = C E A √(2Δp/ρ); C=0.77−0.09β; β from circular-segment h/D; A=(π/4) D² β²; incompressible ε=1; C is reported, not an input\n\nLimitation: C from β, not Re_D; Re_D∈[1e4, 9e6] is the ISO envelope; h/D∈[0.20,0.60]; β∈[0.377,0.791]; D∈[50 mm, 600 mm]; h/D=0.5 → β=√0.5\n\nLimitation: Not cone C=0.82, not ISA 1932 C(β,Re), not RHG orifice, not ISO 5167-4 type C, not long-radius C(β), not given C_d, not Q=Av, not Darcy f, not compressible ε", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_wedge.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D": 0.1, "h": 0.05, "Re_D": 1000000, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.iso_wedge.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/elbow-meter": { "post": { "operationId": "calculate_physics_fluid_elbow_meter", "summary": "Elbow flow meter", "description": "90° elbow tap meter Q=C A √(2Δp/ρ) with C=√((R/D)/2). Not pipe-bend K, not Pitot C=1, not venturi, not ISO 5167-6 wedge, not Q=Av, not Darcy. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.elbow_meter`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: 90° elbow tap meter: Q = C A √(2Δp/ρ); C=√((R/D)/2); A=(π/4)D²; inner/outer radius taps; incompressible; C is reported, not an input\n\nLimitation: R/D∈[1.0, 3.0]; D∈[25 mm, 600 mm]; 90° only; C from R/D, not a given Pitot C=1\n\nLimitation: Not pipe-bend K=0.21 (θ/90)/√(R/D), not Pitot v=C√(2Δp/ρ), not venturi, not ISO 5167-6 wedge, not Q=Av, not Darcy f", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.elbow_meter.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "D": 0.1, "R": 0.15, "dP": 10000, "rho": 1000 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.elbow_meter.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/broad-crested-weir": { "post": { "operationId": "calculate_physics_fluid_broad_crested_weir", "summary": "Broad-crested weir", "description": "Rectangular broad-crested weir Q=C_d (2/3)^{3/2} b √g H^{3/2}, default C_d=0.85. Not thin-plate weir, not Manning, not Q=Av, not orifice, not Francis 3.33. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.broad_crested_weir`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Rectangular broad-crested weir: Q = C_d (2/3)^{3/2} b √g H^{3/2}; default C_d=0.85; modular free nappe; C_d is an input in (0, 1]\n\nLimitation: H is upstream head above the crest, not energy head; optional L_c envelope H/L_c∈[0.08,0.50]; optional P with H/P≤1.5\n\nLimitation: Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not Manning n, not Q=Av, not orifice C_d A √(2gH), not Francis 3.33 L H^{3/2}", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.broad_crested_weir.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "b": 1, "H": 0.2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.broad_crested_weir.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/parshall-flume": { "post": { "operationId": "calculate_physics_fluid_parshall_flume", "summary": "Parshall flume", "description": "USBR 1–8 ft Parshall free-flow Q from throat W and gage Ha, n=1.522 W_ft^{0.026}. Not thin-plate weir, not broad-crested weir, not Manning, not Q=Av, not orifice. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.parshall_flume`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: USBR 1–8 ft Parshall free flow: Q_cfs = 4 W_ft Ha_ft^n, n=1.522 W_ft^{0.026}; SI W, Ha, Q; n is reported, not an input\n\nLimitation: Ha is the specified-gage upstream head, not weir crest head H; W∈[0.3048 m, 2.4384 m]; Ha∈[0.03048 m, 1.6764 m]; free nappe only\n\nLimitation: Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not broad-crested (2/3)^{3/2} b √g H^{3/2}, not Manning n, not Q=Av, not orifice, not submerged Hb", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.parshall_flume.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "W": 0.3048, "Ha": 0.3048 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.parshall_flume.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cutthroat-flume": { "post": { "operationId": "calculate_physics_fluid_cutthroat_flume", "summary": "Cutthroat flume", "description": "Skogerboe cutthroat free-flow Q from throat W, independent length L_f, and gage Ha. Not Parshall, not thin-plate weir, not broad-crested weir, not Manning, not Q=Av, not orifice. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.cutthroat_flume`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Skogerboe cutthroat free flow: Q_cfs = C Ha_ft^n; C=3.50 W_ft^{1.025} (L_f/3 ft)^{0.020}; n=1.56 (L_f/3 ft)^{0.026}; SI W, L_f, Ha, Q; C and n are reported, not inputs\n\nLimitation: No diverging section; L_f is independent flume length, not weir crest L; W < L_f; L_f∈[0.4572 m, 2.7432 m]; W∈[0.0508 m, 1.8288 m]; Ha∈[0.03048 m, 1.2192 m]\n\nLimitation: Not Parshall 4 W_ft Ha^{1.522 W^{0.026}}, not thin-plate weir, not broad-crested (2/3)^{3/2} √g, not Manning n, not Q=Av, not orifice, not submerged Hb", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.cutthroat_flume.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "W": 0.3048, "L_f": 0.9144, "Ha": 0.3048 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.cutthroat_flume.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sluice-gate": { "post": { "operationId": "calculate_physics_fluid_sluice_gate", "summary": "Sluice gate", "description": "Swamee 1992 free-flow undershot sluice Q from opening a, width b, and upstream depth y1. Not tank orifice, not thin-plate weir, not a flume, not Manning, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.sluice_gate`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Swamee 1992 free-flow undershot sluice: Q = C_d a b √(2g y1); C_d = 0.611 [(y1−a)/y1]^{0.072}; SI a, b, y1, Q; C_d is reported, not an input\n\nLimitation: Gate opening a is not orifice area A; y1 is upstream depth, not weir H; a/y1∈[0.05, 0.65]; y1 > a; free flow only\n\nLimitation: Not thin-plate weir, not tank orifice C_d A √(2gH), not a flume, not Manning n, not Q=Av, not submerged y2", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.sluice_gate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "a": 0.2, "b": 1, "y1": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.sluice_gate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ogee-spillway": { "post": { "operationId": "calculate_physics_fluid_ogee_spillway", "summary": "Ogee spillway", "description": "USBR high-overflow ogee Q from crest L, head H, and design head Hd. Not thin-plate weir, not broad-crested weir, not sluice, not Manning, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.ogee_spillway`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: USBR high-overflow ogee: Q_cfs = C L_ft H_ft^{3/2}; C = 3.98 (H/Hd)^{0.12}; SI L, H, Hd, Q; C is reported, not an input\n\nLimitation: H/Hd∈[0.2, 1.33]; optional P with P/Hd≥1.7; vertical upstream face; free overflow\n\nLimitation: Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not broad-crested (2/3)^{3/2} b √g H^{3/2}, not sluice, not Manning n, not Q=Av, not Francis 3.33", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.ogee_spillway.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "L": 1, "H": 1, "Hd": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.ogee_spillway.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/side-weir": { "post": { "operationId": "calculate_physics_fluid_side_weir", "summary": "Side weir", "description": "Borghei 1999 sharp-crested side weir Q from B, L, y1, p, and Q1. Not frontal thin-plate weir, not ogee, not sluice, not Manning, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.side_weir`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Borghei 1999 sharp-crested side weir: Q=(2/3) C_d L √(2g) (y1−p)^{3/2}; C_d=0.71−0.41 Fr₁−0.22(p/y1); SI B, L, y1, p, Q1, Q; C_d is reported\n\nLimitation: Rectangular channel; subcritical Fr₁∈[0.1, 0.9]; p/y1∈[0.1, 0.9]; y1>p; free lateral overflow; De Marchi-type C_d, not a given frontal C_d\n\nLimitation: Not thin-plate frontal weir, not ogee Hd, not sluice a b √(2g y1), not Manning n, not Q=Av, not submerged y2", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.side_weir.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "B": 1, "L": 2, "y1": 0.5, "p": 0.2, "Q1": 0.4 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.side_weir.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/normal-depth": { "post": { "operationId": "calculate_physics_fluid_normal_depth", "summary": "Normal depth", "description": "Rectangular uniform-flow yn from SI Manning with A=b yn and R=b yn/(b+2 yn). Not Manning A,R; not critical depth yc; not specific energy E; not Chezy C; not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.normal_depth`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Rectangular uniform-flow normal depth: invert SI Manning Q=(1/n) A R^{2/3} S^{1/2} with A=b yn, R=b yn/(b+2 yn); yn is unknown; n, S, b given\n\nLimitation: yn/b∈[0.01, 10]; n∈[0.008, 0.15]; S∈[1e-6, 0.1]; SI k=1; geometry is rectangular width b, not A and R\n\nLimitation: Not Manning Q with given A,R; not critical depth yc=(q²/g)^{1/3}; not specific energy E; not Chezy C; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.normal_depth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Q": 1.32807, "b": 2, "n": 0.03, "S": 0.001 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.normal_depth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/submerged-weir": { "post": { "operationId": "calculate_physics_fluid_submerged_weir", "summary": "Submerged weir", "description": "Villemonte rectangular submerged weir: Qs=Qf [1−(H2/H1)^{1.5}]^{0.385} on thin-plate Qf. Not free-flow H only, not ogee Hd, not side weir B+Q1, not Manning n, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.submerged_weir`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Villemonte 1947 rectangular submerged weir: Qs = Qf [1−(H2/H1)^{1.5}]^{0.385}; Qf=(2/3) C_d L √(2g) H1^{3/2}; default C_d=0.62; n=1.5 is not Manning n\n\nLimitation: Requires H1 and H2; H2/H1∈[0.20, 0.95]; H1>H2>0; C_d optional in (0, 1]; SI; rectangular thin-plate only\n\nLimitation: Not free-flow thin-plate H only, not ogee Hd, not side weir B+Q1, not Manning n, not Q=Av, not V-notch", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.submerged_weir.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "L": 1, "H1": 0.3, "H2": 0.15 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.submerged_weir.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/drowned-sluice": { "post": { "operationId": "calculate_physics_fluid_drowned_sluice", "summary": "Drowned sluice", "description": "Swamee 1992 drowned undershot sluice: Q=C_d a b √(2g y1) with C_d from y1, a, and y2. Not free-flow sluice, not Villemonte H1+H2, not tank orifice, not Manning n, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.drowned_sluice`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Swamee 1992 drowned undershot sluice: Q=C_d a b √(2g y1); C_d=θ·0.611[(y1−a)/(y1+15a)]^{0.072}; θ from y1, y2, a; C_d is reported\n\nLimitation: Requires y2; drowned when y1 < 0.81 y2 (y2/a)^{0.72}; a/y1∈[0.05, 0.65]; y1>y2>a; SI\n\nLimitation: Not free-flow sluice without y2, not Villemonte H1+H2 weir, not tank orifice C_d A √(2gH), not Manning n, not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.drowned_sluice.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "a": 0.2, "b": 1, "y1": 1, "y2": 0.8 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.drowned_sluice.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/critical-slope": { "post": { "operationId": "calculate_physics_fluid_critical_slope", "summary": "Critical slope", "description": "Rectangular Sc such that yn=yc. SI Manning at y=yc. Not Manning A,R; not normal-depth yn invert; not critical-depth yc as the product; not Chezy C; not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.critical_slope`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Rectangular critical slope: Sc such that yn=yc; SI Manning at y=yc; yc=(q²/g)^{1/3}; Sc=[n Q/(A R^{2/3})]^2 with A=b yc, R=b yc/(b+2 yc)\n\nLimitation: yc/b∈[0.2, 10] so Sc(yc) is one-to-one; n∈[0.008, 0.15]; Sc∈[1e-6, 0.1]; SI k=1; default g=9.80665\n\nLimitation: Not Manning Q from A,R,S; not normal-depth yn invert; not critical-depth yc as the product; not Chezy C; not Q=Av; not US k=1.486; not trapezoid z", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.critical_slope.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Q": 3.4546, "b": 2, "n": 0.03 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.critical_slope.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/specific-force": { "post": { "operationId": "calculate_physics_fluid_specific_force", "summary": "Specific force", "description": "Rectangular M=Q²/(gA)+A ȳ with ȳ=y/2. Not hydraulic jump y2, not specific energy E, not Froude as the product, not Manning n, not Q=Av, not critical slope Sc. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.specific_force`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Rectangular specific force: M = Q²/(gA) + A ȳ with A=b y and ȳ=y/2; SI; default g=9.80665; M is m²\n\nLimitation: Unknown is M (force mode) or y (depth invert, subcritical y>yc by default); conjugate y_alt is reported; Fr is reported not an input\n\nLimitation: Not hydraulic jump y2 from Fr₁>1; not specific energy E=y+v²/(2g); not Froude as the product; not Manning n; not Q=Av; not critical slope Sc", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.specific_force.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Q": 2, "b": 2, "y": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.specific_force.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/alternate-depth": { "post": { "operationId": "calculate_physics_fluid_alternate_depth", "summary": "Alternate depth", "description": "Rectangular both y from E, Q, b with E=y+Q²/(2gA²). Not specific energy E from y+v, not specific force M, not hydraulic jump y2, not critical depth yc as the product, not Manning n, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.alternate_depth`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Rectangular alternate depths: E = y + Q²/(2g A²) with A=b y; both y_sub>yc and y_superEc=1.5 yc; Fr is reported not an input\n\nLimitation: Not specific energy E from y+v; not specific force M; not hydraulic jump y2 from Fr₁>1; not critical-depth yc as the product; not Manning n; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.alternate_depth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "E": 1.05099, "Q": 2, "b": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.alternate_depth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trapezoidal-critical-depth": { "post": { "operationId": "calculate_physics_fluid_trapezoid_critical_depth", "summary": "Trapezoidal critical depth", "description": "Trapezoid Fr=1 from Q, b, z with Q² T = g A³, A=(b+z y)y, T=b+2 z y. Not rectangular yc=(q²/g)^{1/3}, not yn, not E, not Manning Q, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.trapezoid_critical_depth`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Trapezoid critical depth: Fr=1 with A=(b+z yc) yc and T=b+2 z yc so Q² T = g A³; SI; default g=9.80665; z>0 is run/rise\n\nLimitation: Unknown is yc (depth mode) or Q (discharge invert); vc=√(g A/T) is reported; Fr=1 is the definition, not a Froude wrap\n\nLimitation: Not rectangular yc=(q²/g)^{1/3}; not normal-depth yn; not specific energy E; not Manning n; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_critical_depth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Q": 2, "b": 2, "z": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_critical_depth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trapezoidal-normal-depth": { "post": { "operationId": "calculate_physics_fluid_trapezoid_normal_depth", "summary": "Trapezoidal normal depth", "description": "Trapezoid uniform-flow yn from SI Manning with A=(b+z y)y and P=b+2 y √(1+z²). Not rectangular yn, not trapezoid yc, not Manning A,R, not Chezy C, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.trapezoid_normal_depth`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Trapezoid uniform-flow normal depth: invert SI Manning Q=(1/n) A R^{2/3} S^{1/2} with A=(b+z yn) yn, P=b+2 yn √(1+z²), R=A/P; yn is unknown; n, S, b, z given\n\nLimitation: yn/b∈[0.01, 10]; n∈[0.008, 0.15]; S∈[1e-6, 0.1]; z∈(0, 10]; SI k=1; geometry is b and z, not A and R\n\nLimitation: Not rectangular yn; not trapezoid yc; not Manning Q with given A,R; not Chezy C; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_normal_depth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Q": 2.30256, "b": 2, "z": 1, "n": 0.03, "S": 0.001 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_normal_depth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trapezoidal-specific-energy": { "post": { "operationId": "calculate_physics_fluid_trapezoid_specific_energy", "summary": "Trapezoidal specific energy", "description": "Trapezoid E=y+Q²/(2gA²) with A=(b+z y)y. Not rectangular E=y+v²/(2g), not trapezoid yc, not trapezoid yn, not Manning A,R, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.trapezoid_specific_energy`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Trapezoid specific energy: E=y+Q²/(2g A²) with A=(b+z y)y; SI; default g=9.80665; z>0 is run/rise\n\nLimitation: Unknown is E (energy mode) or Q (discharge invert); v=Q/A is reported; not y invert (that is alternate depth)\n\nLimitation: Not rectangular E=y+v²/(2g); not trapezoid yc; not trapezoid yn; not Manning A,R; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_specific_energy.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "y": 1, "Q": 2, "b": 2, "z": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_specific_energy.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trapezoidal-alternate-depth": { "post": { "operationId": "calculate_physics_fluid_trapezoid_alternate_depth", "summary": "Trapezoidal alternate depth", "description": "Trapezoid both y from E, Q, b, z with E=y+Q²/(2gA²), A=(b+z y)y. Not rectangular alternate depth, not trapezoid E, not trapezoid yc, not trapezoid yn, not Manning n, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.trapezoid_alternate_depth`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Trapezoid alternate depths: E = y + Q²/(2g A²) with A=(b+z y)y; both y_sub>yc and y_super0 is run/rise\n\nLimitation: Unknown is the pair (depths mode) or E (energy invert from one y); E>Ec=yc+D_c/2; Fr is reported not an input\n\nLimitation: Not rectangular alternate depth; not trapezoid E from y+Q; not trapezoid yc as the product; not trapezoid yn; not Manning n; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_alternate_depth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "E": 1.02266, "Q": 2, "b": 2, "z": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_alternate_depth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trapezoidal-hydraulic-jump": { "post": { "operationId": "calculate_physics_fluid_trapezoid_hydraulic_jump", "summary": "Trapezoidal hydraulic jump", "description": "Trapezoid sequent depths from M=Q²/(gA)+A ȳ on A=(b+z y)y. Not rectangular Bélanger, not trapezoid alternate E-pair, not trapezoid yc, not trapezoid yn, not Manning n, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.trapezoid_hydraulic_jump`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Trapezoid hydraulic jump: sequent depths from M=Q²/(gA)+A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; z>0 is run/rise; Fr₁>1\n\nLimitation: Unknown is y2 (sequent) or y1 (upstream invert) or ΔE (energy); Fr is reported not an input; not Bélanger y2/y1=(√(1+8Fr₁²)−1)/2\n\nLimitation: Not rectangular sequent depths; not trapezoid alternate E-pair; not trapezoid yc; not trapezoid yn; not Manning n; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_hydraulic_jump.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "y1": 0.25, "Q": 2, "b": 2, "z": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_hydraulic_jump.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trapezoidal-specific-force": { "post": { "operationId": "calculate_physics_fluid_trapezoid_specific_force", "summary": "Trapezoidal specific force", "description": "Trapezoid specific force M = Q²/(gA) + A ȳ on A=(b+z y)y with ȳ=y(3b+2zy)/(6(b+zy)). Not rectangular ȳ=y/2, not trapezoid sequent y2, not trapezoid specific energy E, not Manning n, not Q=Av. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.trapezoid_specific_force`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Trapezoid specific force: M = Q²/(gA) + A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; M is m²; z>0 is run/rise\n\nLimitation: Unknown is M (force mode) or y (depth invert, subcritical y>yc by default); conjugate y_alt is reported; Fr is reported not an input\n\nLimitation: Not rectangular ȳ=y/2; not trapezoid sequent y2; not trapezoid specific energy E; not Manning n; not Q=Av", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_specific_force.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Q": 2, "b": 2, "z": 1, "y": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_specific_force.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/henderson-hasselbalch": { "post": { "operationId": "calculate_chemistry_acid_base_henderson_hasselbalch", "summary": "Henderson–Hasselbalch", "description": "Buffer pH = pKa + log10([A−]/[HA]). Accepts pKa or Ka. Not ICE and not pH = −log10[H+]. (calculation_version 1.0.1)\n\nSemantic capability: `chemistry.acid_base.henderson_hasselbalch`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Monoprotic buffer pair as given — not ICE equilibrium\n\nLimitation: Not pH = −log10[H+]\n\nLimitation: Not activity coefficients or polyprotic", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/chemistry.acid_base.henderson_hasselbalch.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "pKa": 5, "HA": 0.1, "A": 0.2 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/chemistry.acid_base.henderson_hasselbalch.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mole": { "post": { "operationId": "calculate_chemistry_mole_amount", "summary": "Mole", "description": "Amount n = m/M and N = n·N_A. N_A is CODATA 2018 exact. Not molarity and not Henderson–Hasselbalch. (calculation_version 1.0.1)\n\nSemantic capability: `chemistry.mole.amount`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Lab units g, g/mol, mol\n\nLimitation: Not molarity c=n/V or dilution C1V1=C2V2\n\nLimitation: Not ICE or Henderson–Hasselbalch\n\nLimitation: Does not rewrite /convert/chemistry pair pages", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/chemistry.mole.amount.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "mode": "from_mass", "mass": 36.03, "molar_mass": 18.015 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/chemistry.mole.amount.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/molarity": { "post": { "operationId": "calculate_chemistry_solution_molarity", "summary": "Molarity", "description": "Molarity c = n/V and dilution C1·V1 = C2·V2. Lab units mol, L, mol/L. Not mole n=m/M and not Henderson–Hasselbalch. (calculation_version 1.0.1)\n\nSemantic capability: `chemistry.solution.molarity`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Lab units mol, L, mol/L\n\nLimitation: Not mole n=m/M or Avogadro\n\nLimitation: Not ICE or Henderson–Hasselbalch\n\nLimitation: Dilution needs exactly one of c1, v1, c2, v2 omitted", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/chemistry.solution.molarity.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "mode": "molarity", "amount": 0.5, "volume": 0.25 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/chemistry.solution.molarity.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ph": { "post": { "operationId": "calculate_chemistry_acid_base_ph", "summary": "pH", "description": "Water-ion pH and pOH identities at 25 °C: pH = −log10[H+], pOH = −log10[OH−], pH + pOH = 14. Not Henderson–Hasselbalch and not ICE. (calculation_version 1.0.1)\n\nSemantic capability: `chemistry.acid_base.ph`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Kw = 1e-14 at 25 °C (not temperature-dependent)\n\nLimitation: Not Henderson–Hasselbalch buffer pH\n\nLimitation: Not ICE, activity coefficients, or polyprotic", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/chemistry.acid_base.ph.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": { "mode": "ph_from_h", "h": 0.001 }, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/chemistry.acid_base.ph.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/weak-acid-equilibrium": { "post": { "operationId": "calculate_chemistry_equilibrium_weak_acid", "summary": "Weak-acid ICE", "description": "Monoprotic weak-acid ICE: HA ⇌ H+ + A− from formal C and Ka or pKa. Charge and mass balance; optional water at 25 °C. Reuses math.numerical.root. Not Henderson–Hasselbalch and not pH=−log10[H+] identities. (calculation_version 1.0.4)\n\nSemantic capability: `chemistry.equilibrium.weak_acid`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Monoprotic HA only; not polyprotic, not a weak base, not activity coefficients\n\nLimitation: Not Henderson–Hasselbalch (buffer pair as given)\n\nLimitation: Not the water-ion identity page pH=−log10[H+]\n\nLimitation: Kw = 1e-14 at 25 °C when mode=ice", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/chemistry.equilibrium.weak_acid.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": { "mode": "ice", "C": 0.1, "Ka": 0.000018 }, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/chemistry.equilibrium.weak_acid.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/weak-base-equilibrium": { "post": { "operationId": "calculate_chemistry_equilibrium_weak_base", "summary": "Weak-base ICE", "description": "Monoprotic weak-base ICE: B + H2O ⇌ BH+ + OH− from formal C and Kb or pKb. Charge and mass balance; optional water at 25 °C. Reuses math.numerical.root. Not Henderson–Hasselbalch and not weak-acid ICE. (calculation_version 1.0.4)\n\nSemantic capability: `chemistry.equilibrium.weak_base`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Monoprotic B only; not polyprotic, not a weak acid, not activity coefficients\n\nLimitation: Not Henderson–Hasselbalch (buffer pair as given)\n\nLimitation: Not weak-acid ICE HA ⇌ H+ + A−\n\nLimitation: Not the water-ion identity page pH=−log10[H+]\n\nLimitation: Kw = 1e-14 at 25 °C when mode=ice", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/chemistry.equilibrium.weak_base.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": { "mode": "ice", "C": 0.1, "Kb": 0.000018 }, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/chemistry.equilibrium.weak_base.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/stefan-boltzmann": { "post": { "operationId": "calculate_physics_thermo_stefan_boltzmann", "summary": "Stefan–Boltzmann", "description": "Net gray-body flux q = εσ(Th⁴−Tc⁴). Optional Q = A·q. Not Fourier/Newton heat-transfer and not a view-factor solver. (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.stefan_boltzmann`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Gray body; no view factor (F=1)\n\nLimitation: T in kelvin\n\nLimitation: Not conduction/convection heat-transfer\n\nLimitation: Not heatsink Rth or steam", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.stefan_boltzmann.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "Th": 400, "Tc": 300, "epsilon": 1 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.stefan_boltzmann.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/thermal-resistance": { "post": { "operationId": "calculate_physics_thermo_thermal_resistance", "summary": "Thermal resistance", "description": "Lumped thermal resistance. Conduction R=L/(k A), convection R=1/(h A), series ΣR, parallel 1/R=Σ1/R_i. Optional Q=ΔT/R. Not Fourier/Newton Q, not heatsink θ, not steam, not radiation. (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.thermal_resistance`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Lumped R; SI K/W\n\nLimitation: Series R=ΣR_i; parallel 1/R=Σ1/R_i; Q=ΔT/R when ΔT is given\n\nLimitation: Not Fourier/Newton Q (see /calc/physics/heat-transfer)\n\nLimitation: Not heatsink θJC/θSA, not steam, not radiation", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.thermal_resistance.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "mode": "conduction", "k": 1, "A": 2, "L": 0.5 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.thermal_resistance.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/composite-wall": { "post": { "operationId": "calculate_physics_thermo_composite_wall", "summary": "Composite wall", "description": "Plane composite wall from a layer list. R_i = L_i/(k_i A), optional films 1/(h A), R = R_in + ΣR_i + R_out. Optional Q=ΔT/R. Not Fourier/Newton Q, not lumped R-network, not heatsink θ, not steam, not cylindrical. (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.composite_wall`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Plane wall; 1-D; shared A; SI K/W\n\nLimitation: R_i = L_i/(k_i A); optional films 1/(h A); Q=ΔT/R when ΔT is given\n\nLimitation: Not Fourier/Newton Q (see /calc/physics/heat-transfer)\n\nLimitation: Not lumped R-network (see /calc/physics/thermal-resistance)\n\nLimitation: Not heatsink θJC/θSA, not steam, not cylindrical", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.composite_wall.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": { "k1": 1, "L1": 0.5, "k2": 0.5, "L2": 0.2, "A": 2 }, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.composite_wall.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/bernoulli": { "post": { "operationId": "calculate_physics_fluid_bernoulli", "summary": "Bernoulli's Equation", "description": "Incompressible Bernoulli along a streamline: solve P2, v2, or h2. (calculation_version 1.0.1)\n\nSemantic capability: `physics.fluid.bernoulli`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Incompressible; inviscid; steady streamline; no losses", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.bernoulli.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.bernoulli.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/specific-heat": { "post": { "operationId": "calculate_physics_thermo_specific_heat", "summary": "Specific Heat Capacity", "description": "Q = m c ΔT solve for Q, m, c, or ΔT. (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.specific_heat`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant c; no phase change", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.specific_heat.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.specific_heat.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/newton-lbf": { "post": { "operationId": "calculate_units_force_newton_lbf", "summary": "Newton ↔ lbf", "description": "Force conversion with 1 lbf = 4.4482216152605 N. (calculation_version 1.0.0)\n\nSemantic capability: `units.force.newton_lbf`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact NIST factor", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.force.newton_lbf.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.force.newton_lbf.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/mps-kmh": { "post": { "operationId": "calculate_units_speed_mps_kmh", "summary": "m/s ↔ km/h", "description": "Speed conversion with factor 3.6. (calculation_version 1.0.0)\n\nSemantic capability: `units.speed.mps_kmh`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Non-negative speed", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.speed.mps_kmh.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.speed.mps_kmh.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/suvat": { "post": { "operationId": "calculate_physics_kinematics_suvat", "summary": "SUVAT Calculator", "description": "Constant-acceleration kinematics (SUVAT). (calculation_version 1.0.1)\n\nSemantic capability: `physics.kinematics.suvat`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant a; 1D", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.suvat.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.suvat.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/torque": { "post": { "operationId": "calculate_physics_dynamics_torque", "summary": "Torque Calculator", "description": "τ = r F sinθ. (calculation_version 1.0.0)\n\nSemantic capability: `physics.dynamics.torque`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Single force; planar", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.torque.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.torque.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/free-fall": { "post": { "operationId": "calculate_physics_kinematics_free_fall", "summary": "Free Fall Calculator", "description": "Free fall under constant g (optional initial velocity). (calculation_version 1.0.1)\n\nSemantic capability: `physics.kinematics.free_fall`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: No drag; constant g", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.free_fall.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.free_fall.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/work-power": { "post": { "operationId": "calculate_physics_dynamics_work_power", "summary": "Work and Power Calculator", "description": "W=Fs cosθ and P=W/t or Fv. (calculation_version 1.0.1)\n\nSemantic capability: `physics.dynamics.work_power`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant force; no variable systems", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.work_power.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.work_power.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/flow-rate": { "post": { "operationId": "calculate_physics_fluid_flow_rate", "summary": "Flow Rate Calculator", "description": "Volumetric flow Q=A·v (optional pipe diameter). (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.flow_rate`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Incompressible continuum; uniform velocity", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.flow_rate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.flow_rate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/joule-ev": { "post": { "operationId": "calculate_units_energy_joule_ev", "summary": "Joule ↔ Electronvolt", "description": "Energy conversion with 1 eV = 1.602176634×10⁻¹⁹ J (exact). (calculation_version 1.0.0)\n\nSemantic capability: `units.energy.joule_ev`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact SI factor; no relativistic frames", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.energy.joule_ev.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.energy.joule_ev.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/binary-hex": { "post": { "operationId": "calculate_units_digital_binary_hex", "summary": "Binary ↔ Hexadecimal", "description": "Integer base-2 ↔ base-16 conversion (optional 0b/0x prefixes). (calculation_version 1.0.0)\n\nSemantic capability: `units.digital.binary_hex`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Unsigned integers only; no fractional digits", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/units.digital.binary_hex.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/units.digital.binary_hex.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/velocity": { "post": { "operationId": "calculate_physics_kinematics_velocity", "summary": "Velocity Calculator", "description": "Average velocity v = s/t (solve v, s, or t). (calculation_version 1.0.0)\n\nSemantic capability: `physics.kinematics.velocity`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Average speed along path; 1D", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.velocity.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.velocity.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/momentum": { "post": { "operationId": "calculate_physics_dynamics_momentum", "summary": "Momentum Calculator", "description": "Linear momentum p = m·v (solve p, m, or v). (calculation_version 1.0.0)\n\nSemantic capability: `physics.dynamics.momentum`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Non-relativistic; single particle", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.momentum.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.momentum.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/acceleration": { "post": { "operationId": "calculate_physics_kinematics_acceleration", "summary": "Acceleration Calculator", "description": "Constant acceleration a = (v − u)/t. (calculation_version 1.0.0)\n\nSemantic capability: `physics.kinematics.acceleration`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant a; 1D", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.acceleration.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.acceleration.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/half-life": { "post": { "operationId": "calculate_physics_modern_half_life", "summary": "Half-Life Calculator", "description": "Radioactive decay N = N₀ · 2^(−t/T½). (calculation_version 1.0.0)\n\nSemantic capability: `physics.modern.half_life`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Single exponential; no branching ratios", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.modern.half_life.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.modern.half_life.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/efficiency": { "post": { "operationId": "calculate_physics_energy_efficiency", "summary": "Efficiency Calculator", "description": "η = Pout/Pin as fraction and percent. (calculation_version 1.0.0)\n\nSemantic capability: `physics.energy.efficiency`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: η ≤ 1; no heat-engine Carnot bound", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.energy.efficiency.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.energy.efficiency.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/boyle": { "post": { "operationId": "calculate_physics_thermo_boyle", "summary": "Boyle's Law Calculator", "description": "Isothermal Boyle relation P1·V1 = P2·V2. (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.boyle`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Isothermal only; use Ideal Gas when T changes", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.boyle.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.boyle.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/kinetic": { "post": { "operationId": "calculate_physics_energy_kinetic", "summary": "Kinetic Energy Calculator", "description": "KE = ½mv² (solve KE, m, or v). (calculation_version 1.0.0)\n\nSemantic capability: `physics.energy.kinetic`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Classical; no relativistic KE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.energy.kinetic.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.energy.kinetic.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/potential": { "post": { "operationId": "calculate_physics_energy_potential", "summary": "Potential Energy Calculator", "description": "Gravitational PE = mgh (default g=9.80665). (calculation_version 1.0.0)\n\nSemantic capability: `physics.energy.potential`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Gravitational PE near Earth; not elastic", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.energy.potential.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.energy.potential.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/friction": { "post": { "operationId": "calculate_physics_dynamics_friction", "summary": "Friction Calculator", "description": "F = μN; optional incline N = mg cosθ. (calculation_version 1.0.0)\n\nSemantic capability: `physics.dynamics.friction`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Coulomb model; static vs kinetic μ not distinguished beyond input", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.friction.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.friction.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/doppler": { "post": { "operationId": "calculate_physics_acoustics_doppler", "summary": "Doppler Effect Calculator", "description": "1D acoustic Doppler f′ = f(v±vo)/(v±vs). (calculation_version 1.0.0)\n\nSemantic capability: `physics.acoustics.doppler`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: 1D classical; default air speed 343 m/s", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.acoustics.doppler.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.acoustics.doppler.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/snell": { "post": { "operationId": "calculate_physics_optics_snell", "summary": "Snell's Law Calculator", "description": "n1 sinθ1 = n2 sinθ2 plus critical angle. (calculation_version 1.0.0)\n\nSemantic capability: `physics.optics.snell`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Geometric optics; TIR flagged as error in refraction modes", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.optics.snell.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.optics.snell.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/resistor-color": { "post": { "operationId": "calculate_electrical_resistor_color_code", "summary": "Resistor Color Code Calculator", "description": "IEC 60062 3–6 band decode to ohms, tolerance, TCR. (calculation_version 1.0.0)\n\nSemantic capability: `electrical.resistor_color_code`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Through-hole IEC 60062 colors; not SMD codes", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/electrical.resistor_color_code.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/electrical.resistor_color_code.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/charles": { "post": { "operationId": "calculate_physics_thermo_charles", "summary": "Charles's Law Calculator", "description": "Isobaric Charles relation V1/T1 = V2/T2 (T in kelvin). (calculation_version 1.0.0)\n\nSemantic capability: `physics.thermo.charles`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Isobaric only; temperatures must be absolute (K)", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.charles.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.thermo.charles.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sound-level": { "post": { "operationId": "calculate_physics_acoustics_sound_level", "summary": "Sound Level Calculator", "description": "Intensity and pressure sound levels in dB; incoherent level combination. (calculation_version 1.0.0)\n\nSemantic capability: `physics.acoustics.sound_level`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: I0=1e-12 W/m², p0=20 µPa; no A-weighting", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.acoustics.sound_level.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.acoustics.sound_level.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trajectory": { "post": { "operationId": "calculate_physics_kinematics_trajectory", "summary": "Projectile Trajectory Calculator", "description": "Flat-ground trajectory: range/height/time, position at t, or solve angle. (calculation_version 1.0.0)\n\nSemantic capability: `physics.kinematics.trajectory`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: No drag; level ground", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.trajectory.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.trajectory.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/centripetal": { "post": { "operationId": "calculate_physics_dynamics_centripetal", "summary": "Centripetal Force Calculator", "description": "Fc = mv²/r and a = v²/r. (calculation_version 1.0.0)\n\nSemantic capability: `physics.dynamics.centripetal`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Uniform circular motion; no banked-curve friction", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.centripetal.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.centripetal.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/electric-field": { "post": { "operationId": "calculate_physics_em_electric_field", "summary": "Electric Field Calculator", "description": "Point-charge E, force on q, and potential. (calculation_version 1.0.0)\n\nSemantic capability: `physics.em.electric_field`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Point charge in vacuum; k default 8.9875517923e9", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.em.electric_field.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.em.electric_field.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/faraday": { "post": { "operationId": "calculate_physics_em_faraday", "summary": "Faraday's Law Calculator", "description": "Induced emf magnitude from flux change or B·A. (calculation_version 1.0.0)\n\nSemantic capability: `physics.em.faraday`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Magnitude only (Lenz sign omitted); uniform B over area", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.em.faraday.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.em.faraday.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/lens-maker": { "post": { "operationId": "calculate_physics_optics_lens_maker", "summary": "Lens Maker Calculator", "description": "Lensmaker equation and thin-lens conjugates. (calculation_version 1.0.0)\n\nSemantic capability: `physics.optics.lens_maker`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Thin lens in air; Cartesian sign convention for R", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.optics.lens_maker.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.optics.lens_maker.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/impulse": { "post": { "operationId": "calculate_physics_dynamics_impulse", "summary": "Impulse Calculator", "description": "Impulse J = FΔt = Δp. (calculation_version 1.0.0)\n\nSemantic capability: `physics.dynamics.impulse`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Average force / constant F over Δt", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.impulse.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.dynamics.impulse.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/viscosity": { "post": { "operationId": "calculate_physics_fluid_viscosity", "summary": "Viscosity Calculator", "description": "Dynamic viscosity from shear; kinematic ν = η/ρ. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.viscosity`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Newtonian fluid; constant η", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.viscosity.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.viscosity.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/displacement": { "post": { "operationId": "calculate_physics_kinematics_displacement", "summary": "Displacement Calculator", "description": "1D Δx and 2D displacement magnitude. (calculation_version 1.0.0)\n\nSemantic capability: `physics.kinematics.displacement`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Position change, not path length", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.displacement.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.kinematics.displacement.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/drag": { "post": { "operationId": "calculate_physics_fluid_drag", "summary": "Drag Force Calculator", "description": "Quadratic drag Fd = ½ρv²CdA. (calculation_version 1.0.0)\n\nSemantic capability: `physics.fluid.drag`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Quadratic drag model; Cd treated as constant", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.drag.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.fluid.drag.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/magnetic-field": { "post": { "operationId": "calculate_physics_em_magnetic_field", "summary": "Magnetic Field Calculator", "description": "B for long wire and long solenoid. (calculation_version 1.0.0)\n\nSemantic capability: `physics.em.magnetic_field`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ideal infinite wire / long solenoid", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.em.magnetic_field.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.em.magnetic_field.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/time-dilation": { "post": { "operationId": "calculate_physics_modern_time_dilation", "summary": "Time Dilation Calculator", "description": "Special-relativistic Δt = γΔτ. (calculation_version 1.0.0)\n\nSemantic capability: `physics.modern.time_dilation`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Special relativity only; v < c", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.modern.time_dilation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.modern.time_dilation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/linear-thermal-expansion": { "post": { "operationId": "calculate_materials_thermal_linear_expansion", "summary": "Linear Thermal Expansion Calculator", "description": "Constant-coefficient free linear expansion: delta_length = alpha * initial_length * delta_temperature. (calculation_version 1.0.0)\n\nSemantic capability: `materials.thermal.linear_expansion`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Constant mean alpha over the entered interval\n\nLimitation: Free one-dimensional expansion; no thermal stress\n\nLimitation: No material-property database or automatic coefficient selection", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/materials.thermal.linear_expansion.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/materials.thermal.linear_expansion.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/youngs": { "post": { "operationId": "calculate_physics_materials_youngs", "summary": "Young's Modulus Calculator", "description": "Y = stress/strain for uniaxial elasticity. (calculation_version 1.0.0)\n\nSemantic capability: `physics.materials.youngs`.\n\nCalculation version: `1.0.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Linear elastic regime; isotropic", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.0" ] }, "description": "Pin calculation_version (published: 1.0.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/physics.materials.youngs.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.0", "examples": [ "1.0.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/physics.materials.youngs.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/final-grade": { "post": { "operationId": "calculate_education_final_grade", "summary": "Final grade", "description": "Need-on-final, overall after the exam, weighted categories, and points-to-weight for a fixed final exam share. (calculation_version 1.1.1)\n\nSemantic capability: `education.final_grade`.\n\nCalculation version: `1.1.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Need on final / Overall: Current must exclude the final (pre-final grade). Do not enter an LMS current that already counts the final as 0%.\n\nLimitation: Weighted: enter category grades and weights as they actually appear for completed work; remaining weight is optional.\n\nLimitation: W is percent (40); w = W/100 is the fraction form. Do not mix W and w in one expression.\n\nLimitation: Need on final with W = 0 → status invalid, code WEIGHT_REQUIRED (not a number).\n\nLimitation: Points mode total ≤ 0 → TOTAL_POINTS_REQUIRED. Final points > total still computes and warns POINTS_EXCEED_TOTAL.\n\nLimitation: Letter cutoffs / GPA points are a reference example, not part of the calculation model.\n\nLimitation: Planning estimate only — not an official transcript. No curve, drop-lowest, or extra credit unless you adjust inputs.\n\nLimitation: Engine aliases current/goal/W/finalScore/totalPoints are accepted at runtime; prefer share-URL field names in schemas.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.1" ] }, "description": "Pin calculation_version (published: 1.1.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/education.final_grade.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.1", "examples": [ "1.1.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/education.final_grade.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gpa-to-letter": { "post": { "operationId": "calculate_education_gpa_letter", "summary": "GPA ↔ letter grade", "description": "Approximate GPA↔letter lookup on plus/minus 4.33, flat 4.0, or linear 5.0 normalization. One table, two SEO entries (GPA→letter and letter→GPA). (calculation_version 1.1.3)\n\nSemantic capability: `education.gpa_letter`.\n\nCalculation version: `1.1.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Interpretation of a numeric GPA or a single letter — not a registrar conversion\n\nLimitation: Not a term or cumulative GPA from a course list (use the GPA calculator)\n\nLimitation: Example percentage bands are syllabus conventions, not derived from GPA", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.3" ] }, "description": "Pin calculation_version (published: 1.1.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/education.gpa_letter.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.3", "examples": [ "1.1.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/education.gpa_letter.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/letter-grade-to-gpa": { "post": { "operationId": "calculate_education_gpa_letter_alias_letter_grade_to_gpa", "summary": "GPA ↔ letter grade (letter-grade-to-gpa page alias)", "description": "Approximate GPA↔letter lookup on plus/minus 4.33, flat 4.0, or linear 5.0 normalization. One table, two SEO entries (GPA→letter and letter→GPA). (calculation_version 1.1.3)\n\nSemantic capability: `education.gpa_letter`.\n\nCalculation version: `1.1.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Interpretation of a numeric GPA or a single letter — not a registrar conversion\n\nLimitation: Not a term or cumulative GPA from a course list (use the GPA calculator)\n\nLimitation: Example percentage bands are syllabus conventions, not derived from GPA", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.3" ] }, "description": "Pin calculation_version (published: 1.1.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/education.gpa_letter.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.3", "examples": [ "1.1.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/education.gpa_letter.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vat": { "post": { "operationId": "calculate_finance_vat", "summary": "VAT / GST", "description": "Add or remove a single-rate consumption tax (VAT or GST labeling). Gross = Net × (1 + rate/100); Net = Gross × 100 / (100 + rate). (calculation_version 1.3.0)\n\nSemantic capability: `finance.vat`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Single flat rate on the entered amount\n\nLimitation: No multi-rate baskets, exemptions, or input-tax credits\n\nLimitation: GST page is an SEO entry of this capability — same engine, GST labeling", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/finance.vat.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/finance.vat.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gst": { "post": { "operationId": "calculate_finance_vat_alias_gst", "summary": "VAT / GST (gst page alias)", "description": "Add or remove a single-rate consumption tax (VAT or GST labeling). Gross = Net × (1 + rate/100); Net = Gross × 100 / (100 + rate). (calculation_version 1.3.0)\n\nSemantic capability: `finance.vat`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Single flat rate on the entered amount\n\nLimitation: No multi-rate baskets, exemptions, or input-tax credits\n\nLimitation: GST page is an SEO entry of this capability — same engine, GST labeling", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/finance.vat.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/finance.vat.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/factorial": { "post": { "operationId": "calculate_math_factorial", "summary": "Ordinary factorial", "description": "Exact n! for integers 0 ≤ n ≤ 5000 via BigInt arithmetic, with product expansion, digit count, and scientific notation for long integers. Matching n/nInput aliases; unknown fields rejected. Exactness refers to normalized integer input; numeric JSON rounds to binary64. Scientific preview truncates to12 leading digits; complete decimal digits in exact. (calculation_version 1.0.4)\n\nSemantic capability: `math.factorial`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Ordinary (single) factorial only — not multifactorial and not Γ(n+1) for non-integers\n\nLimitation: Domain is 0 ≤ n ≤ 5000 (product/resource bound, not a mathematical bound)\n\nLimitation: Missing n → MISSING_REQUIRED_INPUT\n\nLimitation: Non-numeric or non-integer n → INVALID_NUMBER\n\nLimitation: n < 0 → VALUE_MUST_BE_NON_NEGATIVE\n\nLimitation: n > 5000 → VALUE_ABOVE_MAX\n\nLimitation: Digits-only strings: trimmed length≤64; matching n/nInput aliases; string scientific notation rejected. JSON numeric finite rounding is permitted; raw nonzero underflow rejected.\n\nLimitation: Scientific display uses the first12 digits without rounding; exact contains every digit.\n\nLimitation: Unknown fields → UNKNOWN_INPUT; aliases disagree → INPUT_ALIAS_CONFLICT; excessive text → INPUT_TOO_LARGE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.factorial.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.factorial.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/fractions": { "post": { "operationId": "calculate_math_fractions", "summary": "Fractions", "description": "Exact safe-integer fraction and signed mixed-number arithmetic (+,−,×,÷), simplification and decimal previews. From decimal converts the shortest normalized binary64 decimal to an exact base10 rational, or rejects an unsafe reduced n/d; no continued-fraction or silent-zero substitute. (calculation_version 1.0.8)\n\nSemantic capability: `math.fractions`.\n\nCalculation version: `1.0.8`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Integer numerators and denominators only (optional mixed-number whole)\n\nLimitation: Denominator 0 → DENOMINATOR_MUST_BE_NONZERO\n\nLimitation: Division by 0/n → DIVISION_BY_ZERO\n\nLimitation: Add/subtract use LCD = LCM(b, d); (ad ± bc)/bd is an equivalent check only\n\nLimitation: Negative sign is normalized onto the numerator after reduction\n\nLimitation: Expert review pending — L1 engine-tested / source-checked\n\nLimitation: Required numerator/denominator or decimal never default; whole alone may be absent/empty. Unknown mode/op/field and conflicting aliases rejected.\n\nLimitation: From-dec uses shortest decimal serialization after binary64 normalization, not the exact binary float fraction. Nonzero-to-zero rejected; reduced numerator and denominator must be safe integers.\n\nLimitation: rational_exact describes n/d; decimal/decimal_display are rounded previews (12 significant digits normally,9 scientific). Full structured result available in native exports.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.8" ] }, "description": "Pin calculation_version (published: 1.0.8); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.fractions.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.8", "examples": [ "1.0.8" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.8" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.fractions.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gcf": { "post": { "operationId": "calculate_math_gcf", "summary": "Greatest common factor", "description": "Exact GCF/GCD/HCF of2–32 signed integers up to48 digits, with bounded working, strict aliases and complete method results. (calculation_version 1.0.3)\n\nSemantic capability: `math.gcf`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Integers only; negatives treated by absolute value\n\nLimitation: Each integer ≤ 48 decimal digits (product bound, not a mathematical bound)\n\nLimitation: Zeros are ignored unless every input is 0 (then UNDEFINED)\n\nLimitation: Need at least two numbers → NEED_TWO_NUMBERS\n\nLimitation: Non-integers → INVALID_NUMBER\n\nLimitation: Integers beyond MAX_SAFE_INTEGER must be decimal strings in JSON\n\nLimitation: At most32 integers; list text≤4096 characters, individual array strings≤128 characters\n\nLimitation: Aliases values/numbers/numsInput must normalize to the same ordered list; unknown fields rejected\n\nLimitation: Exactness refers to accepted integers. Nonzero raw JSON underflow and unsafe numeric integers are rejected.\n\nLimitation: Method agreement is an internal cross-check, not third-party certification.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.gcf.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.gcf.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/lcm": { "post": { "operationId": "calculate_math_lcm", "summary": "Least common multiple", "description": "Exact least common multiple of2–32 signed integers of at most48 decimal digits each. Any zero gives0. Complete working and bounded listing/prime cross-checks; unsafe JSON integers must be decimal strings. (calculation_version 1.0.4)\n\nSemantic capability: `math.lcm`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact relative to accepted normalized integers; cannot recover precision already lost by the client or JSON numeric parsing.\n\nLimitation: 2–32 values,48 decimal digits per integer,4096 list characters; matching ordered aliases required.\n\nLimitation: Listing bound5000 and inputs≤500, at most80 displayed multiples per row with explicit omission; prime cross-check input bound1000000.\n\nLimitation: Result may contain up to1536 decimal digits; summary/full and exports preserve the complete integer.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.lcm.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.lcm.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ratio": { "post": { "operationId": "calculate_math_ratio", "summary": "Ratio", "description": "Simplify, scale, and compare ratios; solve proportions; split a total; convert part-to-part ratios to fraction, decimal, and part-of-whole percent using exact rationals. (calculation_version 1.0.3)\n\nSemantic capability: `math.ratio`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Integers, terminating decimals, and simple a/b fractions only (no mixed numbers or scientific notation)\n\nLimitation: Simplify / proportion / compare allow negative terms\n\nLimitation: All-zero simplify → ALL_ZERO\n\nLimitation: Proportion needs exactly one blank among A,B,C,D → PROPORTION_ONE_BLANK\n\nLimitation: Expert review pending — L1 engine-tested / source-checked\n\nLimitation: Each token≤128 characters;48 digits per integer/decimal or fraction component. Binary64 JSON numbers may already round; unsafe integer numbers rejected; exact strings recommended.\n\nLimitation: Aliases must agree; unknown and nonempty inactive fields rejected.\n\nLimitation: Proportion requires a unique solution and nonzero B,D including solved denominators.\n\nLimitation: Split terms and total must be nonnegative, sum of terms positive.\n\nLimitation: Bars approximate; tiny percentages may be invisible, exact text retained.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.ratio.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.ratio.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/proportion": { "post": { "operationId": "calculate_math_ratio_alias_proportion", "summary": "Ratio (proportion page alias)", "description": "Simplify, scale, and compare ratios; solve proportions; split a total; convert part-to-part ratios to fraction, decimal, and part-of-whole percent using exact rationals. (calculation_version 1.0.3)\n\nSemantic capability: `math.ratio`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Integers, terminating decimals, and simple a/b fractions only (no mixed numbers or scientific notation)\n\nLimitation: Simplify / proportion / compare allow negative terms\n\nLimitation: All-zero simplify → ALL_ZERO\n\nLimitation: Proportion needs exactly one blank among A,B,C,D → PROPORTION_ONE_BLANK\n\nLimitation: Expert review pending — L1 engine-tested / source-checked\n\nLimitation: Each token≤128 characters;48 digits per integer/decimal or fraction component. Binary64 JSON numbers may already round; unsafe integer numbers rejected; exact strings recommended.\n\nLimitation: Aliases must agree; unknown and nonempty inactive fields rejected.\n\nLimitation: Proportion requires a unique solution and nonzero B,D including solved denominators.\n\nLimitation: Split terms and total must be nonnegative, sum of terms positive.\n\nLimitation: Bars approximate; tiny percentages may be invisible, exact text retained.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.ratio.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.ratio.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/log": { "post": { "operationId": "calculate_math_log", "summary": "Logarithm", "description": "Common, natural, and arbitrary-base real logarithms; solve for y, x, or b with change-of-base. (calculation_version 1.1.6)\n\nSemantic capability: `math.log`.\n\nCalculation version: `1.1.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Solve y=log_b(x), x=b^y or b=x^(1/y). Positive finite x and base b>0,b≠1; y finite. Omitted base defaults10 only for forward/argument solve.\n\nLimitation: Strict decimal/scientific text up to512 characters or e; matching known-input aliases; unknown keys, nonfinite types and nonzero text rounded to zero reject. Legacy all-three selects y; requested output fields are ignored.\n\nLimitation: No numerical snapping near1/2/e/10. Symbolic base e uses Math.log/exp; numeric bases preserve binary64 values. Base1 rounding rejects RESULT_ROUNDED_TO_ONE, distinct from no mathematical solution.\n\nLimitation: Independent Decimal200 fixed complete-pack vectors:4ULP for logarithm/argument and128ULP for solved base; known fields exact binary64.16 existing common-log O3 vectors retain2ULP. Neither is a whole-domain guarantee.\n\nLimitation: Display normally12 significant digits, preserving extra digits near1; complete native exports retain raw inputs. Conditioning grows near base1 and y=0 for base solve. Local typing; URL/REST/MCP send inputs and may enter logs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.6" ] }, "description": "Pin calculation_version (published: 1.1.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.log.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.6", "examples": [ "1.1.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.log.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/quadratic": { "post": { "operationId": "calculate_math_quadratic", "summary": "Quadratic formula", "description": "Solve ax² + bx + c = 0, or ax² + bx + c ○ rhs for ○ in {<,≤,>,≥}. Sign of a is the outside of the roots. Inequality discovery /quadratic-inequality. Not cubic, not CAS factoring. (calculation_version 1.1.2)\n\nSemantic capability: `math.quadratic`.\n\nCalculation version: `1.1.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite real binary64 a,b,c with a nonzero; solve or quadratic inequality lt/le/gt/ge. Decimal/scientific,Unicode minus,en-US grouped inputs andinteger fractions supported; each text token <=512characters. Fractions are projected once tobinary64; exact decisions refer toaccepted binary64 values.\n\nLimitation: a/aInput,b/bInput,c/cInput,rhs/d andoperator aliases mustagree. Missing/blank/null required coefficients reject; rawnonzero underflow rejects NUMERIC_UNDERFLOW; unknown keys andinapplicable solve-mode operators/rhs reject. The inequality entry locks mode=inequality.\n\nLimitation: Exact bounded rational discriminant,shifted constant andvertex decisions; scaled square root andstableq roots. Required discriminant/root/vertex projection outside finite binary64 or distinct roots collapsing toonefloat rejects NUMERICAL_RANGE_ERROR. This isnot universal success forfinite coefficients; exact arithmetic bounded16384bits.\n\nLimitation: 65-plus independent CPython Fraction andDecimal800/1100 fullpacks; rootcoordinate ceiling4ULP forfixedvectors,all other numbers/keys/types/presentation strict. Classification/topology exact onaccepted floats. Near multiple roots areillconditioned undercoefficient changes; nocross-runtime/globalULP guarantee.\n\nLimitation: Display preservesnonzero/distinct binary64 values; symbolic factors onlywhen exact reconstruction succeeds. Curve samples useexact rational Horner. Finite-window/cluster/tiny graph omissions areexplicit; fullscalar/interval data andnative JSON/CSV remain. CSV text isformula-neutralized.\n\nLimitation: Typing computeslocally. ShareURLs andREST/MCP transmitinputs andmayenterbrowser/server/intermediary logs. Oldversionlinks warnbeforecurrent execution; historical numerical runtime isnot replayed.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.2" ] }, "description": "Pin calculation_version (published: 1.1.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.quadratic.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.2", "examples": [ "1.1.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.quadratic.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/quadratic-inequality": { "post": { "operationId": "calculate_math_quadratic_alias_quadratic_inequality", "summary": "Quadratic formula (quadratic-inequality page alias)", "description": "Solve ax² + bx + c = 0, or ax² + bx + c ○ rhs for ○ in {<,≤,>,≥}. Sign of a is the outside of the roots. Inequality discovery /quadratic-inequality. Not cubic, not CAS factoring. (calculation_version 1.1.2)\n\nSemantic capability: `math.quadratic`.\n\nCalculation version: `1.1.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite real binary64 a,b,c with a nonzero; solve or quadratic inequality lt/le/gt/ge. Decimal/scientific,Unicode minus,en-US grouped inputs andinteger fractions supported; each text token <=512characters. Fractions are projected once tobinary64; exact decisions refer toaccepted binary64 values.\n\nLimitation: a/aInput,b/bInput,c/cInput,rhs/d andoperator aliases mustagree. Missing/blank/null required coefficients reject; rawnonzero underflow rejects NUMERIC_UNDERFLOW; unknown keys andinapplicable solve-mode operators/rhs reject. The inequality entry locks mode=inequality.\n\nLimitation: Exact bounded rational discriminant,shifted constant andvertex decisions; scaled square root andstableq roots. Required discriminant/root/vertex projection outside finite binary64 or distinct roots collapsing toonefloat rejects NUMERICAL_RANGE_ERROR. This isnot universal success forfinite coefficients; exact arithmetic bounded16384bits.\n\nLimitation: 65-plus independent CPython Fraction andDecimal800/1100 fullpacks; rootcoordinate ceiling4ULP forfixedvectors,all other numbers/keys/types/presentation strict. Classification/topology exact onaccepted floats. Near multiple roots areillconditioned undercoefficient changes; nocross-runtime/globalULP guarantee.\n\nLimitation: Display preservesnonzero/distinct binary64 values; symbolic factors onlywhen exact reconstruction succeeds. Curve samples useexact rational Horner. Finite-window/cluster/tiny graph omissions areexplicit; fullscalar/interval data andnative JSON/CSV remain. CSV text isformula-neutralized.\n\nLimitation: Typing computeslocally. ShareURLs andREST/MCP transmitinputs andmayenterbrowser/server/intermediary logs. Oldversionlinks warnbeforecurrent execution; historical numerical runtime isnot replayed.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.2" ] }, "description": "Pin calculation_version (published: 1.1.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.quadratic.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.2", "examples": [ "1.1.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.quadratic.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/percentage": { "post": { "operationId": "calculate_math_percentage", "summary": "Percentage", "description": "Phrase modes: P% of X, what percent, of-what, percent change, adjust ±P%, and percentage difference. (calculation_version 1.2.0)\n\nSemantic capability: `math.percentage`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact formulas of normalized binary64 inputs, output rounded once ties-to-even. Decimal inputs are rounded binary64, not exact decimal arithmetic.\n\nLimitation: Reject nonzero values that round to zero and overflow (including published delta/average); rescale on NUMERIC_RANGE.\n\nLimitation: Change uses |old|; difference needs nonnegative a,b and nonzero sum. Near zero baseline is ill-conditioned; shortest round-trip display is not significant-figure tracking.\n\nLimitation: At most512 characters per scalar; active fields only and aliases must agree.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.percentage.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.percentage.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/percent-change": { "post": { "operationId": "calculate_math_percent_change", "summary": "Percentage change", "description": "Signed percent change (V₂ − V₁)/|V₁|×100% with reverse solve for V₁ or V₂. (calculation_version 1.2.0)\n\nSemantic capability: `math.percent_change`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Signed change uses |v1|; nonzero initial value required. Inverse preserves both signed branches or infinite/no-solution outcomes.\n\nLimitation: Exact rational expressions of normalized binary64 inputs, one ties-even rounding per published field; not exact decimal measurement arithmetic.\n\nLimitation: Reject nonzero underflow/overflow in inputs, secondary fields or valid candidate branches; no partial candidate set. Rescale. Near±100 inverse percentages are ill-conditioned.\n\nLimitation: 8ULP same-sign nonzero triple consistency, strict zero; preserve requested percent when solving final even if final rounds unchanged.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.percent_change.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.percent_change.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/percent-error": { "post": { "operationId": "calculate_math_percent_error", "summary": "Percent error", "description": "Absolute/signed percent error, complete inverse branches and per-branch diagnostics; binary64 range and resolution policy. (calculation_version 1.2.0)\n\nSemantic capability: `math.percent_error`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: T must be nonzero; quantities need the same ratio-scale unit.\n\nLimitation: Private CPython Fraction reference covers sampled binary64 domains; no measurement uncertainty or exhaustive real-domain proof.\n\nLimitation: Every valid branch/secondary result must fit binary64; NUMERIC_RANGE requires rescaling.\n\nLimitation: Inverse P is requested; achieved P and resolution_limited describe candidate rounding; strict-zero8ULP triple consistency.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.percent_error.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.percent_error.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/pythagorean": { "post": { "operationId": "calculate_math_pythagorean", "summary": "Pythagorean theorem", "description": "Right-triangle solve a² + b² = c² for a missing side, plus area and perimeter; verify mode when all three sides given. (calculation_version 1.2.0)\n\nSemantic capability: `math.pythagorean`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Positive finite binary64 side lengths in consistent units. Decimal text at most512characters,strict types and matching aliases. Nonzero-to-zero conversion rejects.\n\nLimitation: Four operations:c,a,b,verify. solve_for selects the output;all supplied side tokens still validate. All three without solve_for verify;mode=verify conflicts with solve_for.\n\nLimitation: Verification checks nondegenerate geometry and squared relative residual |a²+b²-c²|/c²<=1e-6 with scaled squares. Approximate binary64 diagnostics may differ by2e-15 near the threshold; no exact-equality proof.\n\nLimitation: Solved sides must fit positive finite binary64. Unrepresentable positive area/perimeter are null with explicit range status;invalid verify has no right-angle area. Values display12significant digits. Exact radical only for exactly representable safe-integer radicands.\n\nLimitation: Diagram is schematic,not to scale;no right-angle diagram for failed verification. Browser calculations run locally;shared URLs and REST/MCP transmit inputs and may enter logs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.pythagorean.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.pythagorean.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ln": { "post": { "operationId": "calculate_math_ln", "summary": "Natural logarithm", "description": "Natural logarithm y = ln(x) = log_e(x) for real x > 0, with exp(result) verification. (calculation_version 1.0.5)\n\nSemantic capability: `math.ln`.\n\nCalculation version: `1.0.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Positive finite binary64 x or symbolic e; strict decimal/scientific text ≤512 characters; nonzero text rounded to zero rejects NUMERIC_UNDERFLOW. Unknown keys/conflicting x aliases reject. Legacy y/yInput ignored.\n\nLimitation: Math.log approximates normalized binary64 inputs. Exact flag only x=1 or symbolic e. Display 12 significant digits; native exports retain full pack and input text.\n\nLimitation: Independent Decimal180 vectors accept logarithms within4 ULP and inverse values within16 EPS max(1,|y|) relative plus2 subnormal quanta. Existing16 O3 vectors retain2 ULP; neither claim covers the whole domain.\n\nLimitation: Near1 input rounding is ill conditioned; inverse check tolerance128 EPS max(1,|y|) relative plus2 subnormal quanta is not exactness proof.\n\nLimitation: Typing local; shared URLs/REST/MCP send inputs and may enter logs. Slider0.1–10 only; Focus graph bounded around current input.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.5" ] }, "description": "Pin calculation_version (published: 1.0.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.ln.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.5", "examples": [ "1.0.5" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.ln.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/square-root": { "post": { "operationId": "calculate_math_square_root", "summary": "Square root", "description": "Principal square root of x; non-negative returns real principal, negative returns principal imaginary √|x| i. (calculation_version 1.0.4)\n\nSemantic capability: `math.square_root`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Principal branch on finite real radicands: x≥0 gives real=principal=√x,imag=0; x<0 gives real=0,imag=√|x|,principal=null. Both real/imag/principal are always present.\n\nLimitation: Numbers or strict decimal/scientific strings of at most512 characters; x and xInput must agree. Unknown keys, nonfinite values, null, booleans, hex, commas and nonzero-to-zero underflow reject.\n\nLimitation: Binary64 input rounding and Math.sqrt output rounding are distinct; at most2 ULP on declared independent Decimal2000 reference vectors, not an exhaustive or exact-decimal guarantee. Relative condition number1/2 away from zero; derivative unbounded at zero.\n\nLimitation: 12 significant digit display. Perfect-square claims require safe-integer radicands and roots. Scaled Babylonian working is an illustration, not the engine algorithm.\n\nLimitation: Live graph shows the real branch in a bounded window; negative radicands have no real point. Typing computes locally; shared URLs and REST/MCP send inputs and may enter logs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.square_root.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.square_root.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/anti-log": { "post": { "operationId": "calculate_math_antilog", "summary": "Antilogarithm", "description": "Inverse of log: x = b^y (common, natural, binary, or custom base). (calculation_version 1.0.7)\n\nSemantic capability: `math.antilog`.\n\nCalculation version: `1.0.7`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: x=b^y for finite y and positive finite b≠1. Omitted base defaults10. Scalar output remains unrounded binary64; overflow and result rounding tozero reject.\n\nLimitation: Selected alias precedence: y then yInput; baseId then base; selected explicit preset/numeric base overrides b/baseInput; custom uses b then baseInput; absent base token uses b then baseInput. Nullish aliases fall through. Ignored shadow fields do not change the selected value.\n\nLimitation: Selected numeric text is strict decimal/scientific up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. Explicit blank/invalid base rejects instead of defaulting. Unknown keys reject; compare/digits are validated presentation-only options.\n\nLimitation: Symbolic e means Math.exp(y); numeric/custom Math.E remains binary64 Math.pow. No proximity snapping.51 independent Decimal150/250 scalar references use2ULP fixed-vector budget; existing O3 budget retained, no whole-domain guarantee.\n\nLimitation: Display precision is rounding only. Inverse uses unrounded x and is not independent verification; x rounded to1 cannot recover nonzero y. Conditioning depends on |y| nearbase1 and |y ln b| for exponent perturbations.\n\nLimitation: Typing local; shared URLs/REST/MCP send inputs and may enter logs. Native exports retain scalar output and raw provided inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.7" ] }, "description": "Pin calculation_version (published: 1.0.7); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.antilog.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.7", "examples": [ "1.0.7" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.7" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.antilog.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/root": { "post": { "operationId": "calculate_math_root", "summary": "Nth root", "description": "Principal real nth root of a with positive safe-integer index n (default 2). (calculation_version 1.0.6)\n\nSemantic capability: `math.root`.\n\nCalculation version: `1.0.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Principal real nth root only. Even index requires a≥0 (NOT_REAL otherwise); odd-negative uses the real negative branch, distinct from complex principal powers.\n\nLimitation: Strict decimal/scientific text up to512 characters; reject unknown keys, nonfinite, null, hex, comma, mismatching aliases, nonzero text rounded to zero. Exact positive safe-integer index; omitted index defaults to2, explicit blank/null rejects. Semantic cross-field and exact-text rules run after Schema shape validation.\n\nLimitation: Binary64 identity for n=1, Math.sqrt for n=2, Math.cbrt for n=3, signed Math.pow for higher indices. Declared fixed references have≤64 ULP overall; existing path-specific O3 vectors retain0/2/64 ULP. Not a whole-domain guarantee or exact-decimal result.\n\nLimitation: Relative condition number in radicand is1/n away from zero; derivative singular at zero for n>1. Input rounding, reciprocal-exponent error and root rounding are distinct. Raising rounded output to n can overflow or amplify error.\n\nLimitation: 12 significant digit display; exports keep full binary64 scalar, raw inputs and calculation version. Bounded real graph; typing computes locally, shared URLs and REST/MCP send inputs and may enter logs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.6" ] }, "description": "Pin calculation_version (published: 1.0.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.root.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.6", "examples": [ "1.0.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.root.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/exponent": { "post": { "operationId": "calculate_math_exponent", "summary": "Exponentiation", "description": "Real power y = aⁿ with solve_for y (default scalar), a, or n. (calculation_version 1.0.5)\n\nSemantic capability: `math.exponent`.\n\nCalculation version: `1.0.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real power equation y=a^n. solve_for y/a/n; omit the unknown and provide exactly the two known fields. Omitted mode inferred from the two fields. Matching aliases only, unknown keys reject.\n\nLimitation: Strict decimal/scientific tokens up to512 characters; null/blank/nonfinite/hex/boolean reject; nonzero text rounded to zero rejects NUMERIC_UNDERFLOW. Raw JSON numeric underflow rejects before parse loss. Integer exponent must be an exact safe integer. Semantic constraints follow shape validation.\n\nLimitation: Only symbolic e uses exp/log; numeric approximations retain their own value. Negative-base forward domain requires integer n; inverse n for negative bases requires an integer reproducing signed y. Base -1 gives infinitely many integer exponents for y=±1. Inverse even integer powers preserve both signs.\n\nLimitation: Binary64, not exact decimal. Independent fixed review vectors allow16 ULP forward/log-ratio and128 ULP inverse-base reciprocal powers; legacy O3 six vectors retain2 ULP. Not a whole-domain guarantee. Forward relative sensitivity |n| in a; inverse exponent ill-conditioned near a=1. Subnormal results have low relative accuracy. Overflow/nonzero-to-zero results reject.\n\nLimitation: 12 significant digit display, full typed outputs/raw inputs/version in exports. Negative-base graphs do not draw a continuous real curve. Typing local; shared URLs/REST/MCP send inputs and may enter logs; links run current version.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.5" ] }, "description": "Pin calculation_version (published: 1.0.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.exponent.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.5", "examples": [ "1.0.5" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.exponent.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sin": { "post": { "operationId": "calculate_math_sin", "summary": "Sine", "description": "sin(θ) in degrees (default) or radians, with algebraic snap for textbook angles. (calculation_version 1.1.0)\n\nSemantic capability: `math.sin`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Angle mode: finite binary64 theta; a nonzero degree sine rounding tozero rejects RESULT_UNDERFLOW; deg(default) or rad. Degree reduction uses signed remainder before quadrant reduction; no add360 or angle-proximity epsilon. Listed common degree angles and 17 normalized binary64 radian tokens within ±2π use symbolic recognition, not mathematical exactness of floating-point radians.\n\nLimitation: Ratio mode: finite opposite≥0, hypotenuse>0 and opposite≤hypotenuse; returns opposite/hypotenuse. A nonzero ratio rounding tozero rejects RESULT_UNDERFLOW. Angle fields in ratio mode and side fields in angle mode reject UNEXPECTED_INPUT.\n\nLimitation: Numeric aliases theta/t/angle/thetaInput, opposite/oppInput and hypotenuse/hypInput must agree; unit/unitInput normalize degree(s)/°/radian(s), case/space accepted. Missing mode defaultsangle. Unknown keys reject. Explicit null/blank numeric fields reject; null/blank unit defaultsdeg.\n\nLimitation: Strict decimal/scientific source text ≤512 characters; hexadecimal, booleans and grouped numbers reject. Nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. RawJSON numbers are checked before lossy parse; finite subnormal accepted.\n\nLimitation: Independent Decimal420/620 Taylor/Machin and Fraction references:2ULP fixed-vector ceiling; zero/sign/types strict. Legacy18 O3 samples retain2ULP budget; no whole-domain or cross-runtime bitwise guarantee. Radian generic path uses Math.sin; degrees reduced before conversion.\n\nLimitation: Nearzeros relative conditioning is unbounded; large input spacing loses source angle information before computation. Sine may legitimately round to±1. Display12significant digits falls back tofull binary64 if rounding changes a boundary. Native exports preserve full scalar and raw inputs.\n\nLimitation: Graph omitted in ratio mode and for |theta|>1e6; diagram/derived angle is not independent verification. Typing local; sharedURLs/REST/MCP send inputs and may enter logs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.sin.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.sin.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cos": { "post": { "operationId": "calculate_math_cos", "summary": "Cosine", "description": "cos(θ) in degrees (default) or radians, with algebraic snap for textbook angles. (calculation_version 1.1.0)\n\nSemantic capability: `math.cos`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Angle mode: finite binary64 theta; deg(default) or rad. Degree reduction uses signed remainder before quadrant reduction; no add360 or angle-proximity epsilon. Listed common degree angles and 17 normalized binary64 radian tokens within ±2π use symbolic recognition, not mathematical exactness of floating-point radians.\n\nLimitation: Ratio mode: finite adjacent≥0, hypotenuse>0 and adjacent≤hypotenuse; returns adjacent/hypotenuse. A nonzero ratio rounding tozero rejects RESULT_UNDERFLOW. Angle fields in ratio mode and side fields in angle mode reject UNEXPECTED_INPUT.\n\nLimitation: Numeric aliases theta/t/angle/thetaInput, adjacent/adjInput and hypotenuse/hypInput must agree; unit/unitInput normalize degree(s)/°/radian(s), case/space accepted. Missing mode defaultsangle. Unknown keys reject. Explicit null/blank numeric fields reject; null/blank unit defaultsdeg.\n\nLimitation: Strict decimal/scientific source text ≤512 characters; hexadecimal, booleans and grouped numbers reject. Nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. RawJSON numbers are checked before lossy parse; finite subnormal accepted.\n\nLimitation: Independent Decimal420/620 Taylor/Machin and Fraction references:2ULP fixed-vector ceiling; zero/sign/types strict. Legacy18 O3 samples retain2ULP budget; no whole-domain or cross-runtime bitwise guarantee. Radian generic path uses Math.cos; degrees reduced before conversion.\n\nLimitation: Nearzeros relative conditioning is unbounded; large input spacing loses source angle information before computation. Cosine may legitimately round to±1. Display12significant digits falls back tofull binary64 if rounding changes a boundary. Native exports preserve full scalar and raw inputs.\n\nLimitation: Graph omitted in ratio mode and for |theta|>1e6; diagram/derived angle is not independent verification. Typing local; sharedURLs/REST/MCP send inputs and may enter logs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.cos.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.cos.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/tan": { "post": { "operationId": "calculate_math_tan", "summary": "Tangent", "description": "tan(θ) in degrees (default) or radians; exact odd multiples of 90° are UNDEFINED; near-pole returns finite with NEAR_SINGULARITY. (calculation_version 1.1.0)\n\nSemantic capability: `math.tan`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite binary64 angle;deg(default) orrad. Strict decimal/scientific text<=512characters;unknownkeys/conflictingaliases reject. Null/blank numeric rejects;null/blankunit defaultsdeg. Nonzero source text rounding0 rejectsNUMERIC_UNDERFLOW.\n\nLimitation: Degree reduction before conversion,stable tan/cotangent offsets;exact odd90degree poles rejectUNDEFINED without epsilon.17 listed normalized binary64 radian magnitudes within2pi andsignedcounterparts use symbolic recognition;only pi/2 and3pi/2 pole tokens andtheir negatives reject. Genericradians useMath.tan.\n\nLimitation: Nonzero finite input producingzero rejectsRESULT_UNDERFLOW except declaredsymboliczero identities. Nonfinite result rejectsRESULT_OVERFLOW. Finite output is scalar;|value|>5729.57789313059 returns{value,warnings:[NEAR_SINGULARITY]}.\n\nLimitation: 121 independent Decimal420/620 Taylor/Machin referencevectors:2ULPfixedvector budget;zero/sign/types/warnings strict,actualULP reported;16legacyO3values retainedseparately. Noall-domain/cross-runtime guarantee. Nearpoles inputuncertainty strongly amplifies;huge inputspacing losesphase beforecomputation.\n\nLimitation: Display12significantdigits fallsbacktofullbinary64 if rounding erases nonzero orchanges±1. Fullscalar/warnings/rawinputs preservedin native exports. Graph omitted when|theta|>1e6 or|value|>8,not calculation failure.\n\nLimitation: Inverse tangent usespublished Arctan capability viaexplicitnavigation. Typinglocal;shareURLs/REST/MCP sendinputs andmayenterlogs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.tan.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.tan.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/arcsin": { "post": { "operationId": "calculate_math_arcsin", "summary": "Arcsine", "description": "Principal arcsin(x) for x ∈ [−1, 1], returning degrees and radians with verification. (calculation_version 1.1.0)\n\nSemantic capability: `math.arcsin`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: x outside [−1, 1] → NOT_REAL\n\nLimitation: Missing x → MISSING_REQUIRED_INPUT\n\nLimitation: Near-common-value hint is display metadata; it does not replace the canonical deg/rad or assert mathematical exactness.\n\nLimitation: Raw input accepts finite JSON numbers or decimal strings; normalized inputs contain numeric x only. Nonzero text rounded to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Unknown inputs are UNKNOWN_INPUT; x/xInput conflicts are AMBIGUOUS_INPUT.\n\nLimitation: Legacy engine test counts are separate from the CVP Manifest suite. CVP identity is included; production status requires the linked report matched by version, revision and digest.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.arcsin.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.arcsin.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/arccos": { "post": { "operationId": "calculate_math_arccos", "summary": "Arccosine", "description": "Principal arccos(x) for x ∈ [−1, 1], returning degrees and radians with verification. (calculation_version 1.1.0)\n\nSemantic capability: `math.arccos`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: x outside [−1, 1] → NOT_REAL\n\nLimitation: Missing x → MISSING_REQUIRED_INPUT\n\nLimitation: Near-common-value hint is display metadata; it does not replace the canonical deg/rad or assert mathematical exactness.\n\nLimitation: Raw input accepts finite JSON numbers or decimal strings; normalized inputs contain numeric x only. Nonzero text rounded to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Unknown inputs are UNKNOWN_INPUT; x/xInput conflicts are AMBIGUOUS_INPUT.\n\nLimitation: Legacy engine test counts are separate from the CVP Manifest suite. CVP identity is included; production status requires the linked report matched by version, revision and digest.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.arccos.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.arccos.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/arctan": { "post": { "operationId": "calculate_math_arctan", "summary": "Arctangent", "description": "Principal arctan(x) for any finite real x, returning degrees and radians with verification. (calculation_version 1.1.0)\n\nSemantic capability: `math.arctan`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Missing x → MISSING_REQUIRED_INPUT\n\nLimitation: Non-finite → INVALID_NUMBER\n\nLimitation: Near-common-value hint is display metadata; it does not replace the canonical deg/rad or assert mathematical exactness.\n\nLimitation: Raw input accepts finite JSON numbers or decimal strings; normalized inputs contain numeric x only. Nonzero text rounded to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Unknown inputs are UNKNOWN_INPUT; x/xInput conflicts are AMBIGUOUS_INPUT.\n\nLimitation: Legacy engine test counts are separate from the CVP Manifest suite. CVP identity is included; production status requires the linked report matched by version, revision and digest.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.arctan.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.arctan.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/add": { "post": { "operationId": "calculate_math_sum", "summary": "Sum / addition", "description": "Exact decimal totals and rational means; scientific lists use finite Neumaier binary64; bounded Long addition shows complete place-value carry work. (calculation_version 1.0.3)\n\nSemantic capability: `math.sum`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Plain decimals:48 significant digits and48 fractional places;10000 values,65536 total characters,512 per token. Long:32 nonnegative plain decimals and48 aligned columns.\n\nLimitation: sumStr/display are exact only for plain decimals and Long. Numeric fields/chart are binary64 conveniences; mean_rational_exact describes the source and numeric approximation flags describe representation. Repeating means round half away to4 decimal places.\n\nLimitation: Any scientific token selects Neumaier binary64. Conversion, cancellation and intermediate range affect results; no universal ULP guarantee. Nonzero underflow and nonfinite intermediates rejected.\n\nLimitation: Commas separate values, including apparent thousands groups, which issue a warning. Units are not parsed. Share links use the current engine; historical runtimes are not retained.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.sum.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.sum.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/subtraction": { "post": { "operationId": "calculate_math_subtraction", "summary": "Subtraction", "description": "Solve any missing subtraction term with binary64, or exact non-negative decimal Long subtraction with borrowing up to48 aligned columns. (calculation_version 1.0.2)\n\nSemantic capability: `math.subtraction`.\n\nCalculation version: `1.0.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Difference requires exactly two terms and uses binary64, not exact decimal arithmetic. All normalized integral operands must be safe integers. Cancellation may amplify input/conversion error; measurement uncertainty is not modeled.\n\nLimitation: Long uses exact decimal strings; display and exact_value are authoritative. Numeric fields are approximate binary64 conveniences. Up to48 aligned columns, non-negative inputs, negative result allowed; no scientific notation.\n\nLimitation: Tokens at most512 characters, without commas. Unknown fields, invalid types/modes, conflicting aliases and text nonzero underflow rejected.\n\nLimitation: Shared links run the current engine; they do not retain historical runtimes.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.2" ] }, "description": "Pin calculation_version (published: 1.0.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.subtraction.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.2", "examples": [ "1.0.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.subtraction.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/division": { "post": { "operationId": "calculate_math_divide", "summary": "Division", "description": "Binary64 quotient with0–16 display places, or exact non-negative integer long division and full working up to48 digits. (calculation_version 1.0.7)\n\nSemantic capability: `math.divide`.\n\nCalculation version: `1.0.7`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Quotient exact/display_exact refer to normalized binary64 operands and rounded display separately; decimal parsing is not exact decimal arithmetic.\n\nLimitation: All integral quotient operands must fit±(2^53−1). Use Long mode with non-negative integer strings for larger values, up to48 digits.\n\nLimitation: Tokens at most512 characters; unknown fields, mode/type errors and conflicting aliases rejected. Nonzero text/JSON/result underflow is rejected; subnormal nonzero values accepted.\n\nLimitation: Division by zero and overflow rejected. Decimal places default8 when absent/blank, otherwise integer0–16.\n\nLimitation: Share URLs restore current-engine inputs; not a historical runtime.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.7" ] }, "description": "Pin calculation_version (published: 1.0.7); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.divide.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.7", "examples": [ "1.0.7" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.7" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.divide.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/exponential-growth": { "post": { "operationId": "calculate_math_exponential_growth", "summary": "Exponential growth / decay", "description": "Periodic x₀(1+r/100)^t or continuous x₀e^(kt) growth and decay. Any three of x₀, r/k, t, x(t) solve the fourth; all four verify displayed-precision consistency. (calculation_version 1.1.0)\n\nSemantic capability: `math.exponential_growth`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Periodic x(t)=x0(1+r/100)^t requires r>-100%; continuous x(t)=x0 exp(k t) uses ratePct=k per time unit, not percent. Signed amplitudes allowed; inverse time/rate require matching nonzero signs.\n\nLimitation: Provide any three fields or four to compare calculated xt using display quantization. Zero rate/time can make inverses undefined or nonunique. Blank/null fields are missing.\n\nLimitation: Strict decimal/scientific text up to512 characters; nonzero input rounding tozero rejects NUMERIC_UNDERFLOW. Conflicting aliases/unknown fields/models reject. Output is finite unrounded binary64; overflow/underflow reject.\n\nLimitation: Independent Decimal1200/1600 fixed vectors use predeclared4e-12 relative budget plus2 subnormal quanta, strictzero/sign/type. Legacy O3 remains separately tested32ULP. No whole-domain or cross-runtime guarantee; inverse conditioning degrades at zero rate/time and amplitude ratios near1.\n\nLimitation: Typing local; shared URLs, REST and MCP transmit inputs and may enter logs. Native exports retain scalar and provided raw inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.exponential_growth.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": { "x0": 50, "ratePct": 4, "t": 90 }, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.exponential_growth.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/scientific-notation": { "post": { "operationId": "calculate_math_scientific_notation", "summary": "Scientific notation", "description": "Convert between decimal and scientific/engineering notation; normalize and operate on A×10ⁿ forms. (calculation_version 2.0.1)\n\nSemantic capability: `math.scientific_notation`.\n\nCalculation version: `2.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Canonical Agent modes are convert / engineering / normalize / operate. dec-sci, sci-dec, numInput, coefInput, expInput, aInput, bInput are URL/engine adapter aliases, not the Agent contract.\n\nLimitation: Missing/invalid numbers → INVALID_NUMBER / MISSING_REQUIRED_INPUT\n\nLimitation: Division by zero in operate → DIVISION_BY_ZERO\n\nLimitation: Each numeric text token is at most512 characters. Normalize exponent is an integer within±10000. Decimal exponents in A×10^n are combined before one binary64 conversion; finite nonzero subnormals accepted; nonzero values rounded to zero are rejected.\n\nLimitation: Matching adapter aliases only; inactive/unknown fields and invalid mode/op are rejected. Shortest binary64 decimal display does not preserve significant figures. Shared URLs reach the server.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "2.0.1" ] }, "description": "Pin calculation_version (published: 2.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.scientific_notation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 2.0.1", "examples": [ "2.0.1" ] } } }, "example": { "inputs": {}, "calculation_version": "2.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.scientific_notation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/multiplication": { "post": { "operationId": "calculate_math_multiplication", "summary": "Multiplication", "description": "Exact decimal product of multiplicand × multiplier, with optional long-multiplication work. (calculation_version 1.0.4)\n\nSemantic capability: `math.multiplication`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exactness applies to accepted plain decimal tokens, not values rounded by a client before sending. Unsafe JSON integer numbers rejected; strings preserve full source digits.\n\nLimitation: 512 characters and48 significant digits per factor; trailing zeros count.\n\nLimitation: Long grid limited to24 significant digits and24 displayed digit places per normalized factor; otherwise no work, LONG_GRID_TRUNCATED, and full exact product.\n\nLimitation: productStr is authoritative; product is approximate or null on binary64 range loss. Share links use current engine, not historical replay.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.multiplication.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.multiplication.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/combinatorics": { "post": { "operationId": "calculate_math_combinatorics", "summary": "Permutations and combinations", "description": "Exact P(n,k) and C(n,k) for integers 0 ≤ k ≤ n ≤ 1000 via the multiplicative formula. Not a factorial product page. (calculation_version 1.0.3)\n\nSemantic capability: `math.combinatorics`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Distinct items without replacement;0<=k<=n<=1000. k>n is rejected, even though some mathematical libraries extend C(n,k)=0 beyond this product domain.\n\nLimitation: Safe JSON integers or integer strings with at most4digits/512characters; aliases must agree; strict types and unknown keys.\n\nLimitation: Exact count uses BigInt. Counts above18digits have explicitly approximate8-significant-digit previews; full exact counts, formula and working are exported.\n\nLimitation: Not multinomials, with-replacement counts or a standalone factorial tool. JSON numeric literals obey IEEE-754 transport before safe-integer validation; raw nonzero-to-zero underflow is rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.combinatorics.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.combinatorics.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/modulo": { "post": { "operationId": "calculate_math_modulo", "summary": "Euclidean remainder / modular inverse", "description": "Exact Euclidean remainder/quotient and modular inverse for signed integers; canonical Bézout coefficients satisfy the original-input identity. (calculation_version 1.1.2)\n\nSemantic capability: `math.modulo`.\n\nCalculation version: `1.1.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Integer tokens up to48 digits and512 characters; JSON numeric integers must be safe. Use digit strings for larger exact integers; no decimal/scientific syntax.\n\nLimitation: Euclidean0<=r<|m|; nonzero modulus. Inverse requires |m|>=2 and gcd(a,m)=1. Canonical bezout_x=inverse, bezout_y=(1-a*inverse)/modulus.\n\nLimitation: Numeric outputs are safe integers; larger exact values use decimal strings. No floating rounding or measurement-uncertainty model. Not constant-time cryptography.\n\nLimitation: Share links use the current engine. The modular-inverse entry locks inverse, overriding a conflicting mode parameter.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.2" ] }, "description": "Pin calculation_version (published: 1.1.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.modulo.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.2", "examples": [ "1.1.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.modulo.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/modular-inverse": { "post": { "operationId": "calculate_math_modulo_alias_modular_inverse", "summary": "Euclidean remainder / modular inverse (modular-inverse page alias)", "description": "Exact Euclidean remainder/quotient and modular inverse for signed integers; canonical Bézout coefficients satisfy the original-input identity. (calculation_version 1.1.2)\n\nSemantic capability: `math.modulo`.\n\nCalculation version: `1.1.2`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Integer tokens up to48 digits and512 characters; JSON numeric integers must be safe. Use digit strings for larger exact integers; no decimal/scientific syntax.\n\nLimitation: Euclidean0<=r<|m|; nonzero modulus. Inverse requires |m|>=2 and gcd(a,m)=1. Canonical bezout_x=inverse, bezout_y=(1-a*inverse)/modulus.\n\nLimitation: Numeric outputs are safe integers; larger exact values use decimal strings. No floating rounding or measurement-uncertainty model. Not constant-time cryptography.\n\nLimitation: Share links use the current engine. The modular-inverse entry locks inverse, overriding a conflicting mode parameter.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.2" ] }, "description": "Pin calculation_version (published: 1.1.2); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.modulo.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.2", "examples": [ "1.1.2" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.2" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.modulo.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sequence": { "post": { "operationId": "calculate_math_sequences", "summary": "Integer sequences", "description": "Arithmetic and geometric sequences, Fibonacci (F_0=0), and linear recurrences. Exact BigInt. Discovery pages share this capability. Not Pascal, not partition, not n!. Engine id is sequence — never arithmetic. (calculation_version 1.0.3)\n\nSemantic capability: `math.sequences`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact integer arithmetic for four modes;AP/GP n=1..1000,Fibonacci/recurrence n=0..1000. Coefficients at most48 digits,rawtokens at most512 characters,index at most4 digits.\n\nLimitation: Digit strings only;unsafe JSON numbers rejected. Aliases must agree;unknown andinactive inputs rejected. Results use JSON numbers only within safe integers, otherwise exact decimal strings.\n\nLimitation: 37 independent Python integer-enumeration/matrix-power full packs;exact complete structure/type/metadata comparison,notthird-party certification.\n\nLimitation: Large orindistinguishable exact terms omit graph explicitly;fullintegers remain inresult/work/nativeexports. Continuousreal-valued ornonintegersequences unsupported.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/arithmetic-sequence": { "post": { "operationId": "calculate_math_sequences_alias_arithmetic_sequence", "summary": "Integer sequences (arithmetic-sequence page alias)", "description": "Arithmetic and geometric sequences, Fibonacci (F_0=0), and linear recurrences. Exact BigInt. Discovery pages share this capability. Not Pascal, not partition, not n!. Engine id is sequence — never arithmetic. (calculation_version 1.0.3)\n\nSemantic capability: `math.sequences`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact integer arithmetic for four modes;AP/GP n=1..1000,Fibonacci/recurrence n=0..1000. Coefficients at most48 digits,rawtokens at most512 characters,index at most4 digits.\n\nLimitation: Digit strings only;unsafe JSON numbers rejected. Aliases must agree;unknown andinactive inputs rejected. Results use JSON numbers only within safe integers, otherwise exact decimal strings.\n\nLimitation: 37 independent Python integer-enumeration/matrix-power full packs;exact complete structure/type/metadata comparison,notthird-party certification.\n\nLimitation: Large orindistinguishable exact terms omit graph explicitly;fullintegers remain inresult/work/nativeexports. Continuousreal-valued ornonintegersequences unsupported.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/geometric-sequence": { "post": { "operationId": "calculate_math_sequences_alias_geometric_sequence", "summary": "Integer sequences (geometric-sequence page alias)", "description": "Arithmetic and geometric sequences, Fibonacci (F_0=0), and linear recurrences. Exact BigInt. Discovery pages share this capability. Not Pascal, not partition, not n!. Engine id is sequence — never arithmetic. (calculation_version 1.0.3)\n\nSemantic capability: `math.sequences`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact integer arithmetic for four modes;AP/GP n=1..1000,Fibonacci/recurrence n=0..1000. Coefficients at most48 digits,rawtokens at most512 characters,index at most4 digits.\n\nLimitation: Digit strings only;unsafe JSON numbers rejected. Aliases must agree;unknown andinactive inputs rejected. Results use JSON numbers only within safe integers, otherwise exact decimal strings.\n\nLimitation: 37 independent Python integer-enumeration/matrix-power full packs;exact complete structure/type/metadata comparison,notthird-party certification.\n\nLimitation: Large orindistinguishable exact terms omit graph explicitly;fullintegers remain inresult/work/nativeexports. Continuousreal-valued ornonintegersequences unsupported.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/fibonacci": { "post": { "operationId": "calculate_math_sequences_alias_fibonacci", "summary": "Integer sequences (fibonacci page alias)", "description": "Arithmetic and geometric sequences, Fibonacci (F_0=0), and linear recurrences. Exact BigInt. Discovery pages share this capability. Not Pascal, not partition, not n!. Engine id is sequence — never arithmetic. (calculation_version 1.0.3)\n\nSemantic capability: `math.sequences`.\n\nCalculation version: `1.0.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Exact integer arithmetic for four modes;AP/GP n=1..1000,Fibonacci/recurrence n=0..1000. Coefficients at most48 digits,rawtokens at most512 characters,index at most4 digits.\n\nLimitation: Digit strings only;unsafe JSON numbers rejected. Aliases must agree;unknown andinactive inputs rejected. Results use JSON numbers only within safe integers, otherwise exact decimal strings.\n\nLimitation: 37 independent Python integer-enumeration/matrix-power full packs;exact complete structure/type/metadata comparison,notthird-party certification.\n\nLimitation: Large orindistinguishable exact terms omit graph explicitly;fullintegers remain inresult/work/nativeexports. Continuousreal-valued ornonintegersequences unsupported.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.3" ] }, "description": "Pin calculation_version (published: 1.0.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.3", "examples": [ "1.0.3" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.sequences.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/prime-factorization": { "post": { "operationId": "calculate_math_prime_factorization", "summary": "Prime factorization", "description": "Exact bounded prime factorization and primality with sorted factors/exponents, complete counts and empty-product handling for1. (calculation_version 1.0.1)\n\nSemantic capability: `math.prime_factorization`.\n\nCalculation version: `1.0.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: 1<=n<=10^12; integer strings at most13 digits and512 characters, or safe JSON integers. Exactness starts at the normalized integer.\n\nLimitation: n=1 has empty factors and is neither prime nor composite. Factors are sorted ascending; ω counts distinct primes and Ω counts multiplicity.\n\nLimitation: Trial division bounded by sqrt(n); no floating convergence or cryptographic-size factorization service. Primality is a view of the complete factorization.\n\nLimitation: Unknown keys, alias conflicts and invalid types reject. Share links execute the current engine. JSON numeric source follows the general binary64 transport policy; use digit strings for exact source input.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.1" ] }, "description": "Pin calculation_version (published: 1.0.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.prime_factorization.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.1", "examples": [ "1.0.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.0.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.prime_factorization.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/linear-equation": { "post": { "operationId": "calculate_math_algebra_linear_equation", "summary": "Linear equation", "description": "Solve ax + b = rhs, ax + b ○ rhs, |ax + b| = rhs, |ax + b| ○ rhs, (ax + b)/(cx + d) = rhs, or (ax + b)/(cx + d) ○ rhs. a = 0 is identity/inconsistent or ℝ/∅. Discovery /linear-inequality, /absolute-value, /absolute-value-inequality, /rational-equation, /rational-inequality. Not the quadratic formula, not a system, not CAS. (calculation_version 1.5.1)\n\nSemantic capability: `math.algebra.linear_equation`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One variable:linear equation/inequality,absolute equation/inequality,rational equation/inequality. Accepted coefficients are finite binary64; exact rational decisions use those rounded inputs, not arbitrary-precision raw decimals.\n\nLimitation: Strict decimal/scientific text up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. a andrhs required,b defaults0; rational c,d default0 andcannot bothzero. Nonrational c/d are rhs aliases andmust agree. Unknown keys,conflicts,invalid modes/relations andexplicit blank fields reject.\n\nLimitation: Returned solution ranges preserve open/closed endpoints andexcluded poles. No epsilon zero/pole/root merging. Endpoints are rounded once tobinary64; overflow/underflow ordistinct exact boundaries collapsing toonebinary64 value reject explicitly. Exact arithmetic is bounded to16384 numerator/denominator bits.\n\nLimitation: 178 independent Fraction predicate/open-cell references compare complete result packs. One-ULP numerical ceiling for listed vectors; current full serialized comparisons are strict. No whole-domain/cross-runtime guarantee. Display/native result pack remain separate.\n\nLimitation: Six discovery entries lock their documented mode exceptthe canonical page,which accepts all modes. Typing local;share/REST/MCP transmit data andmay enter logs. Real screen reader user-deferred.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/linear-inequality": { "post": { "operationId": "calculate_math_algebra_linear_equation_alias_linear_inequality", "summary": "Linear equation (linear-inequality page alias)", "description": "Solve ax + b = rhs, ax + b ○ rhs, |ax + b| = rhs, |ax + b| ○ rhs, (ax + b)/(cx + d) = rhs, or (ax + b)/(cx + d) ○ rhs. a = 0 is identity/inconsistent or ℝ/∅. Discovery /linear-inequality, /absolute-value, /absolute-value-inequality, /rational-equation, /rational-inequality. Not the quadratic formula, not a system, not CAS. (calculation_version 1.5.1)\n\nSemantic capability: `math.algebra.linear_equation`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One variable:linear equation/inequality,absolute equation/inequality,rational equation/inequality. Accepted coefficients are finite binary64; exact rational decisions use those rounded inputs, not arbitrary-precision raw decimals.\n\nLimitation: Strict decimal/scientific text up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. a andrhs required,b defaults0; rational c,d default0 andcannot bothzero. Nonrational c/d are rhs aliases andmust agree. Unknown keys,conflicts,invalid modes/relations andexplicit blank fields reject.\n\nLimitation: Returned solution ranges preserve open/closed endpoints andexcluded poles. No epsilon zero/pole/root merging. Endpoints are rounded once tobinary64; overflow/underflow ordistinct exact boundaries collapsing toonebinary64 value reject explicitly. Exact arithmetic is bounded to16384 numerator/denominator bits.\n\nLimitation: 178 independent Fraction predicate/open-cell references compare complete result packs. One-ULP numerical ceiling for listed vectors; current full serialized comparisons are strict. No whole-domain/cross-runtime guarantee. Display/native result pack remain separate.\n\nLimitation: Six discovery entries lock their documented mode exceptthe canonical page,which accepts all modes. Typing local;share/REST/MCP transmit data andmay enter logs. Real screen reader user-deferred.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/absolute-value": { "post": { "operationId": "calculate_math_algebra_linear_equation_alias_absolute_value", "summary": "Linear equation (absolute-value page alias)", "description": "Solve ax + b = rhs, ax + b ○ rhs, |ax + b| = rhs, |ax + b| ○ rhs, (ax + b)/(cx + d) = rhs, or (ax + b)/(cx + d) ○ rhs. a = 0 is identity/inconsistent or ℝ/∅. Discovery /linear-inequality, /absolute-value, /absolute-value-inequality, /rational-equation, /rational-inequality. Not the quadratic formula, not a system, not CAS. (calculation_version 1.5.1)\n\nSemantic capability: `math.algebra.linear_equation`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One variable:linear equation/inequality,absolute equation/inequality,rational equation/inequality. Accepted coefficients are finite binary64; exact rational decisions use those rounded inputs, not arbitrary-precision raw decimals.\n\nLimitation: Strict decimal/scientific text up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. a andrhs required,b defaults0; rational c,d default0 andcannot bothzero. Nonrational c/d are rhs aliases andmust agree. Unknown keys,conflicts,invalid modes/relations andexplicit blank fields reject.\n\nLimitation: Returned solution ranges preserve open/closed endpoints andexcluded poles. No epsilon zero/pole/root merging. Endpoints are rounded once tobinary64; overflow/underflow ordistinct exact boundaries collapsing toonebinary64 value reject explicitly. Exact arithmetic is bounded to16384 numerator/denominator bits.\n\nLimitation: 178 independent Fraction predicate/open-cell references compare complete result packs. One-ULP numerical ceiling for listed vectors; current full serialized comparisons are strict. No whole-domain/cross-runtime guarantee. Display/native result pack remain separate.\n\nLimitation: Six discovery entries lock their documented mode exceptthe canonical page,which accepts all modes. Typing local;share/REST/MCP transmit data andmay enter logs. Real screen reader user-deferred.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/absolute-value-inequality": { "post": { "operationId": "calculate_math_algebra_linear_equation_alias_absolute_value_inequality", "summary": "Linear equation (absolute-value-inequality page alias)", "description": "Solve ax + b = rhs, ax + b ○ rhs, |ax + b| = rhs, |ax + b| ○ rhs, (ax + b)/(cx + d) = rhs, or (ax + b)/(cx + d) ○ rhs. a = 0 is identity/inconsistent or ℝ/∅. Discovery /linear-inequality, /absolute-value, /absolute-value-inequality, /rational-equation, /rational-inequality. Not the quadratic formula, not a system, not CAS. (calculation_version 1.5.1)\n\nSemantic capability: `math.algebra.linear_equation`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One variable:linear equation/inequality,absolute equation/inequality,rational equation/inequality. Accepted coefficients are finite binary64; exact rational decisions use those rounded inputs, not arbitrary-precision raw decimals.\n\nLimitation: Strict decimal/scientific text up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. a andrhs required,b defaults0; rational c,d default0 andcannot bothzero. Nonrational c/d are rhs aliases andmust agree. Unknown keys,conflicts,invalid modes/relations andexplicit blank fields reject.\n\nLimitation: Returned solution ranges preserve open/closed endpoints andexcluded poles. No epsilon zero/pole/root merging. Endpoints are rounded once tobinary64; overflow/underflow ordistinct exact boundaries collapsing toonebinary64 value reject explicitly. Exact arithmetic is bounded to16384 numerator/denominator bits.\n\nLimitation: 178 independent Fraction predicate/open-cell references compare complete result packs. One-ULP numerical ceiling for listed vectors; current full serialized comparisons are strict. No whole-domain/cross-runtime guarantee. Display/native result pack remain separate.\n\nLimitation: Six discovery entries lock their documented mode exceptthe canonical page,which accepts all modes. Typing local;share/REST/MCP transmit data andmay enter logs. Real screen reader user-deferred.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/rational-equation": { "post": { "operationId": "calculate_math_algebra_linear_equation_alias_rational_equation", "summary": "Linear equation (rational-equation page alias)", "description": "Solve ax + b = rhs, ax + b ○ rhs, |ax + b| = rhs, |ax + b| ○ rhs, (ax + b)/(cx + d) = rhs, or (ax + b)/(cx + d) ○ rhs. a = 0 is identity/inconsistent or ℝ/∅. Discovery /linear-inequality, /absolute-value, /absolute-value-inequality, /rational-equation, /rational-inequality. Not the quadratic formula, not a system, not CAS. (calculation_version 1.5.1)\n\nSemantic capability: `math.algebra.linear_equation`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One variable:linear equation/inequality,absolute equation/inequality,rational equation/inequality. Accepted coefficients are finite binary64; exact rational decisions use those rounded inputs, not arbitrary-precision raw decimals.\n\nLimitation: Strict decimal/scientific text up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. a andrhs required,b defaults0; rational c,d default0 andcannot bothzero. Nonrational c/d are rhs aliases andmust agree. Unknown keys,conflicts,invalid modes/relations andexplicit blank fields reject.\n\nLimitation: Returned solution ranges preserve open/closed endpoints andexcluded poles. No epsilon zero/pole/root merging. Endpoints are rounded once tobinary64; overflow/underflow ordistinct exact boundaries collapsing toonebinary64 value reject explicitly. Exact arithmetic is bounded to16384 numerator/denominator bits.\n\nLimitation: 178 independent Fraction predicate/open-cell references compare complete result packs. One-ULP numerical ceiling for listed vectors; current full serialized comparisons are strict. No whole-domain/cross-runtime guarantee. Display/native result pack remain separate.\n\nLimitation: Six discovery entries lock their documented mode exceptthe canonical page,which accepts all modes. Typing local;share/REST/MCP transmit data andmay enter logs. Real screen reader user-deferred.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/rational-inequality": { "post": { "operationId": "calculate_math_algebra_linear_equation_alias_rational_inequality", "summary": "Linear equation (rational-inequality page alias)", "description": "Solve ax + b = rhs, ax + b ○ rhs, |ax + b| = rhs, |ax + b| ○ rhs, (ax + b)/(cx + d) = rhs, or (ax + b)/(cx + d) ○ rhs. a = 0 is identity/inconsistent or ℝ/∅. Discovery /linear-inequality, /absolute-value, /absolute-value-inequality, /rational-equation, /rational-inequality. Not the quadratic formula, not a system, not CAS. (calculation_version 1.5.1)\n\nSemantic capability: `math.algebra.linear_equation`.\n\nCalculation version: `1.5.1`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One variable:linear equation/inequality,absolute equation/inequality,rational equation/inequality. Accepted coefficients are finite binary64; exact rational decisions use those rounded inputs, not arbitrary-precision raw decimals.\n\nLimitation: Strict decimal/scientific text up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. a andrhs required,b defaults0; rational c,d default0 andcannot bothzero. Nonrational c/d are rhs aliases andmust agree. Unknown keys,conflicts,invalid modes/relations andexplicit blank fields reject.\n\nLimitation: Returned solution ranges preserve open/closed endpoints andexcluded poles. No epsilon zero/pole/root merging. Endpoints are rounded once tobinary64; overflow/underflow ordistinct exact boundaries collapsing toonebinary64 value reject explicitly. Exact arithmetic is bounded to16384 numerator/denominator bits.\n\nLimitation: 178 independent Fraction predicate/open-cell references compare complete result packs. One-ULP numerical ceiling for listed vectors; current full serialized comparisons are strict. No whole-domain/cross-runtime guarantee. Display/native result pack remain separate.\n\nLimitation: Six discovery entries lock their documented mode exceptthe canonical page,which accepts all modes. Typing local;share/REST/MCP transmit data andmay enter logs. Real screen reader user-deferred.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.5.1" ] }, "description": "Pin calculation_version (published: 1.5.1); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.5.1", "examples": [ "1.5.1" ] } } }, "example": { "inputs": {}, "calculation_version": "1.5.1" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/triangle-solver": { "post": { "operationId": "calculate_math_geometry_triangle", "summary": "Triangle solver", "description": "Solve a Euclidean triangle from SSS, SAS, ASA, AAS, or SSA (ambiguous). Not the Pythagorean-only page. (calculation_version 1.1.0)\n\nSemantic capability: `math.geometry.triangle`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: One consistent length unit, area in its square; angles in degrees. a/b/c opposite A/B/C. Euclidean only.\n\nLimitation: Strict decimal inputs normalize to binary64. SSS inequality classification uses exact dyadic predicates; no fixed absolute length epsilon.\n\nLimitation: SSA no solution -> INVALID_INPUT; one/two solutions retain complete ordered solutions array, acute B before supplementary B. Primary top-level fields mirror solutions[0].\n\nLimitation: Nonzero inputs and reported positive values must be finite normal binary64; rescale on NUMERIC_RANGE. Degree-to-radian values must also remain normal.\n\nLimitation: NUMERIC_CONDITION rejects unresolved triangles: for non-exact SSA sine, abs(a^2-h^2)/(a^2+h^2)<=1e-8 with h=b*sin(A); exact degree30/90/150 sine identities bypass that guard.\n\nLimitation: For derived sides (SAS/ASA/AAS/SSA), each rounded triangle-inequality gap must exceed64*Number.EPSILON times the shortest side. SSS raw-side classification uses exact dyadic inequalities without that guard.\n\nLimitation: Near flat/SSA tangent cases are sensitive to input rounding. Relative5e-10 arithmetic verification against independent high precision is not an input perturbation or universal geometric accuracy guarantee.\n\nLimitation: Browser interaction local; shared URLs and REST/MCP send parameters to the server.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.triangle.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.triangle.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/complex": { "post": { "operationId": "calculate_math_complex", "summary": "Complex numbers", "description": "Rectangular and polar complex arithmetic, integer powers, nth roots, and Euler form. Not a CAS. (calculation_version 1.3.0)\n\nSemantic capability: `math.complex`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite decimal inputs; matching aliases only. Missing rectangular components default0; explicit empty inputs are errors.\n\nLimitation: Power integer |n|≤1000; roots integer2≤n≤64; zero has one distinct root;0^0 undefined.\n\nLimitation: Argument in degrees (−180,180]; negative real axis assigned+180 including signed zero; origin0 by convention (undefined mathematically).\n\nLimitation: Nonzero input/output components and modulus must be normal finite binary64; unrepresentable scaling/intermediates return NUMERIC_RANGE.\n\nLimitation: Vector error budget2e-11 times modulus, argument2e-9 degrees away from ill-conditioned origin/cut; cancellation can lose relative component accuracy.\n\nLimitation: No symbolic CAS or complex noninteger powers.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.complex.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.complex.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/complex-polar": { "post": { "operationId": "calculate_math_complex_alias_complex_polar", "summary": "Complex numbers (complex-polar page alias)", "description": "Rectangular and polar complex arithmetic, integer powers, nth roots, and Euler form. Not a CAS. (calculation_version 1.3.0)\n\nSemantic capability: `math.complex`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite decimal inputs; matching aliases only. Missing rectangular components default0; explicit empty inputs are errors.\n\nLimitation: Power integer |n|≤1000; roots integer2≤n≤64; zero has one distinct root;0^0 undefined.\n\nLimitation: Argument in degrees (−180,180]; negative real axis assigned+180 including signed zero; origin0 by convention (undefined mathematically).\n\nLimitation: Nonzero input/output components and modulus must be normal finite binary64; unrepresentable scaling/intermediates return NUMERIC_RANGE.\n\nLimitation: Vector error budget2e-11 times modulus, argument2e-9 degrees away from ill-conditioned origin/cut; cancellation can lose relative component accuracy.\n\nLimitation: No symbolic CAS or complex noninteger powers.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.complex.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.complex.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/complex-power": { "post": { "operationId": "calculate_math_complex_alias_complex_power", "summary": "Complex numbers (complex-power page alias)", "description": "Rectangular and polar complex arithmetic, integer powers, nth roots, and Euler form. Not a CAS. (calculation_version 1.3.0)\n\nSemantic capability: `math.complex`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite decimal inputs; matching aliases only. Missing rectangular components default0; explicit empty inputs are errors.\n\nLimitation: Power integer |n|≤1000; roots integer2≤n≤64; zero has one distinct root;0^0 undefined.\n\nLimitation: Argument in degrees (−180,180]; negative real axis assigned+180 including signed zero; origin0 by convention (undefined mathematically).\n\nLimitation: Nonzero input/output components and modulus must be normal finite binary64; unrepresentable scaling/intermediates return NUMERIC_RANGE.\n\nLimitation: Vector error budget2e-11 times modulus, argument2e-9 degrees away from ill-conditioned origin/cut; cancellation can lose relative component accuracy.\n\nLimitation: No symbolic CAS or complex noninteger powers.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.complex.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.complex.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/complex-roots": { "post": { "operationId": "calculate_math_complex_alias_complex_roots", "summary": "Complex numbers (complex-roots page alias)", "description": "Rectangular and polar complex arithmetic, integer powers, nth roots, and Euler form. Not a CAS. (calculation_version 1.3.0)\n\nSemantic capability: `math.complex`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite decimal inputs; matching aliases only. Missing rectangular components default0; explicit empty inputs are errors.\n\nLimitation: Power integer |n|≤1000; roots integer2≤n≤64; zero has one distinct root;0^0 undefined.\n\nLimitation: Argument in degrees (−180,180]; negative real axis assigned+180 including signed zero; origin0 by convention (undefined mathematically).\n\nLimitation: Nonzero input/output components and modulus must be normal finite binary64; unrepresentable scaling/intermediates return NUMERIC_RANGE.\n\nLimitation: Vector error budget2e-11 times modulus, argument2e-9 degrees away from ill-conditioned origin/cut; cancellation can lose relative component accuracy.\n\nLimitation: No symbolic CAS or complex noninteger powers.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.complex.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.complex.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/complex-euler": { "post": { "operationId": "calculate_math_complex_alias_complex_euler", "summary": "Complex numbers (complex-euler page alias)", "description": "Rectangular and polar complex arithmetic, integer powers, nth roots, and Euler form. Not a CAS. (calculation_version 1.3.0)\n\nSemantic capability: `math.complex`.\n\nCalculation version: `1.3.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Finite decimal inputs; matching aliases only. Missing rectangular components default0; explicit empty inputs are errors.\n\nLimitation: Power integer |n|≤1000; roots integer2≤n≤64; zero has one distinct root;0^0 undefined.\n\nLimitation: Argument in degrees (−180,180]; negative real axis assigned+180 including signed zero; origin0 by convention (undefined mathematically).\n\nLimitation: Nonzero input/output components and modulus must be normal finite binary64; unrepresentable scaling/intermediates return NUMERIC_RANGE.\n\nLimitation: Vector error budget2e-11 times modulus, argument2e-9 degrees away from ill-conditioned origin/cut; cancellation can lose relative component accuracy.\n\nLimitation: No symbolic CAS or complex noninteger powers.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.3.0" ] }, "description": "Pin calculation_version (published: 1.3.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.complex.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.3.0", "examples": [ "1.3.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.3.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.complex.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/circle": { "post": { "operationId": "calculate_math_geometry_circle", "summary": "Circle", "description": "Radius, diameter, circumference, area, arc length, and sector area of a Euclidean circle. Discovery /sector, /arc. Not the Pythagorean page, not /spherical-sector, not CAS. (calculation_version 1.2.0)\n\nSemantic capability: `math.geometry.circle`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not a²+b²=c² — use /calc/math/pythagorean\n\nLimitation: r ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: Spherical geometry is out of scope\n\nLimitation: All nonzero outputs must be finite normal binary64 values (magnitude at least 2^-1022); exact zero angles are supported. Outside this envelope, NUMERIC_RANGE requests rescaling instead of returning zero, Infinity, or NaN.\n\nLimitation: Raw/normalized inputs follow separate schemas. Nonzero decimal text rounded to zero is NUMERIC_UNDERFLOW; unknown inputs are UNKNOWN_INPUT and conflicting aliases are AMBIGUOUS_INPUT.\n\nLimitation: Legacy engine test counts are separate from CVP. Responses carry the current CVP identity and an exact-match production attestation lookup; no old CURRENT status is inherited.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.circle.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.circle.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sector": { "post": { "operationId": "calculate_math_geometry_circle_alias_sector", "summary": "Circle (sector page alias)", "description": "Radius, diameter, circumference, area, arc length, and sector area of a Euclidean circle. Discovery /sector, /arc. Not the Pythagorean page, not /spherical-sector, not CAS. (calculation_version 1.2.0)\n\nSemantic capability: `math.geometry.circle`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not a²+b²=c² — use /calc/math/pythagorean\n\nLimitation: r ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: Spherical geometry is out of scope\n\nLimitation: All nonzero outputs must be finite normal binary64 values (magnitude at least 2^-1022); exact zero angles are supported. Outside this envelope, NUMERIC_RANGE requests rescaling instead of returning zero, Infinity, or NaN.\n\nLimitation: Raw/normalized inputs follow separate schemas. Nonzero decimal text rounded to zero is NUMERIC_UNDERFLOW; unknown inputs are UNKNOWN_INPUT and conflicting aliases are AMBIGUOUS_INPUT.\n\nLimitation: Legacy engine test counts are separate from CVP. Responses carry the current CVP identity and an exact-match production attestation lookup; no old CURRENT status is inherited.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.circle.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.circle.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/arc": { "post": { "operationId": "calculate_math_geometry_circle_alias_arc", "summary": "Circle (arc page alias)", "description": "Radius, diameter, circumference, area, arc length, and sector area of a Euclidean circle. Discovery /sector, /arc. Not the Pythagorean page, not /spherical-sector, not CAS. (calculation_version 1.2.0)\n\nSemantic capability: `math.geometry.circle`.\n\nCalculation version: `1.2.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not a²+b²=c² — use /calc/math/pythagorean\n\nLimitation: r ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: Spherical geometry is out of scope\n\nLimitation: All nonzero outputs must be finite normal binary64 values (magnitude at least 2^-1022); exact zero angles are supported. Outside this envelope, NUMERIC_RANGE requests rescaling instead of returning zero, Infinity, or NaN.\n\nLimitation: Raw/normalized inputs follow separate schemas. Nonzero decimal text rounded to zero is NUMERIC_UNDERFLOW; unknown inputs are UNKNOWN_INPUT and conflicting aliases are AMBIGUOUS_INPUT.\n\nLimitation: Legacy engine test counts are separate from CVP. Responses carry the current CVP identity and an exact-match production attestation lookup; no old CURRENT status is inherited.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.0" ] }, "description": "Pin calculation_version (published: 1.2.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.circle.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.0", "examples": [ "1.2.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.2.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.circle.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/conic-section": { "post": { "operationId": "calculate_math_geometry_conic", "summary": "Conic section", "description": "Axis-aligned ellipse, parabola, and hyperbola. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page, not coordinate geometry, not CAS. (calculation_version 1.1.0)\n\nSemantic capability: `math.geometry.conic`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Axis-aligned standard forms only; not rotated (xy term), not translated\n\nLimitation: Not the circle-only calculator — a=b is a valid ellipse with e=0; /calc/math/circle stays the circle page\n\nLimitation: Not coordinate geometry (two-point line / intersection / angle)\n\nLimitation: Ellipse perimeter is Ramanujan I, not a complete elliptic integral\n\nLimitation: a ≤ 0 or b ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: parabola p = 0 → INVALID_INPUT\n\nLimitation: unknown mode (including cas, circle, pythagorean) → INVALID_MODE\n\nLimitation: Decimal inputs normalize to binary64; circle uses exact a===b after normalization. Near-circle c/e are sensitive to input rounding; noncircle eccentricity may round to1.\n\nLimitation: Nonzero input/output scalars must be finite normal binary64; NUMERIC_RANGE requires rescaling. No absolute-zero clamp. Explicit empty/null inputs reject; inactive supplied numeric fields are validated.\n\nLimitation: Ellipse perimeter is Ramanujan I approximation, not exact arclength. Relative2e-12 verification compares the stated approximation formula, not its model error.\n\nLimitation: Local browser calculation; shared URLs are received by the server; REST/MCP send their inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ellipse": { "post": { "operationId": "calculate_math_geometry_conic_alias_ellipse", "summary": "Conic section (ellipse page alias)", "description": "Axis-aligned ellipse, parabola, and hyperbola. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page, not coordinate geometry, not CAS. (calculation_version 1.1.0)\n\nSemantic capability: `math.geometry.conic`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Axis-aligned standard forms only; not rotated (xy term), not translated\n\nLimitation: Not the circle-only calculator — a=b is a valid ellipse with e=0; /calc/math/circle stays the circle page\n\nLimitation: Not coordinate geometry (two-point line / intersection / angle)\n\nLimitation: Ellipse perimeter is Ramanujan I, not a complete elliptic integral\n\nLimitation: a ≤ 0 or b ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: parabola p = 0 → INVALID_INPUT\n\nLimitation: unknown mode (including cas, circle, pythagorean) → INVALID_MODE\n\nLimitation: Decimal inputs normalize to binary64; circle uses exact a===b after normalization. Near-circle c/e are sensitive to input rounding; noncircle eccentricity may round to1.\n\nLimitation: Nonzero input/output scalars must be finite normal binary64; NUMERIC_RANGE requires rescaling. No absolute-zero clamp. Explicit empty/null inputs reject; inactive supplied numeric fields are validated.\n\nLimitation: Ellipse perimeter is Ramanujan I approximation, not exact arclength. Relative2e-12 verification compares the stated approximation formula, not its model error.\n\nLimitation: Local browser calculation; shared URLs are received by the server; REST/MCP send their inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/parabola": { "post": { "operationId": "calculate_math_geometry_conic_alias_parabola", "summary": "Conic section (parabola page alias)", "description": "Axis-aligned ellipse, parabola, and hyperbola. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page, not coordinate geometry, not CAS. (calculation_version 1.1.0)\n\nSemantic capability: `math.geometry.conic`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Axis-aligned standard forms only; not rotated (xy term), not translated\n\nLimitation: Not the circle-only calculator — a=b is a valid ellipse with e=0; /calc/math/circle stays the circle page\n\nLimitation: Not coordinate geometry (two-point line / intersection / angle)\n\nLimitation: Ellipse perimeter is Ramanujan I, not a complete elliptic integral\n\nLimitation: a ≤ 0 or b ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: parabola p = 0 → INVALID_INPUT\n\nLimitation: unknown mode (including cas, circle, pythagorean) → INVALID_MODE\n\nLimitation: Decimal inputs normalize to binary64; circle uses exact a===b after normalization. Near-circle c/e are sensitive to input rounding; noncircle eccentricity may round to1.\n\nLimitation: Nonzero input/output scalars must be finite normal binary64; NUMERIC_RANGE requires rescaling. No absolute-zero clamp. Explicit empty/null inputs reject; inactive supplied numeric fields are validated.\n\nLimitation: Ellipse perimeter is Ramanujan I approximation, not exact arclength. Relative2e-12 verification compares the stated approximation formula, not its model error.\n\nLimitation: Local browser calculation; shared URLs are received by the server; REST/MCP send their inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/hyperbola": { "post": { "operationId": "calculate_math_geometry_conic_alias_hyperbola", "summary": "Conic section (hyperbola page alias)", "description": "Axis-aligned ellipse, parabola, and hyperbola. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page, not coordinate geometry, not CAS. (calculation_version 1.1.0)\n\nSemantic capability: `math.geometry.conic`.\n\nCalculation version: `1.1.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Axis-aligned standard forms only; not rotated (xy term), not translated\n\nLimitation: Not the circle-only calculator — a=b is a valid ellipse with e=0; /calc/math/circle stays the circle page\n\nLimitation: Not coordinate geometry (two-point line / intersection / angle)\n\nLimitation: Ellipse perimeter is Ramanujan I, not a complete elliptic integral\n\nLimitation: a ≤ 0 or b ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: parabola p = 0 → INVALID_INPUT\n\nLimitation: unknown mode (including cas, circle, pythagorean) → INVALID_MODE\n\nLimitation: Decimal inputs normalize to binary64; circle uses exact a===b after normalization. Near-circle c/e are sensitive to input rounding; noncircle eccentricity may round to1.\n\nLimitation: Nonzero input/output scalars must be finite normal binary64; NUMERIC_RANGE requires rescaling. No absolute-zero clamp. Explicit empty/null inputs reject; inactive supplied numeric fields are validated.\n\nLimitation: Ellipse perimeter is Ramanujan I approximation, not exact arclength. Relative2e-12 verification compares the stated approximation formula, not its model error.\n\nLimitation: Local browser calculation; shared URLs are received by the server; REST/MCP send their inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.0" ] }, "description": "Pin calculation_version (published: 1.1.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.0", "examples": [ "1.1.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.conic.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/coordinate-geometry": { "post": { "operationId": "calculate_math_geometry_coordinate", "summary": "Coordinate geometry", "description": "Distance, midpoint, slope, two-point line, point-line distance, line intersection, and angle in the plane. Slope is not share-key m. Discovery /line-equation, /point-line-distance, /line-intersection, /angle-between-lines. Not Pythagorean, not CAS. (calculation_version 1.8.0)\n\nSemantic capability: `math.geometry.coordinate`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cartesian R²; all coordinates use one consistent length unit; angle outputs include radians and degrees.\n\nLimitation: Strict decimal inputs; matching x0/px and y0/py aliases; unknown fields reject. Omitted mode defaults distance. Discovery entry URLs lock their documented operation.\n\nLimitation: Exact dyadic predicates classify the supplied normalized binary64 values; decimal-to-binary rounding still affects nearly parallel lines and input-sensitive intersections. No absolute geometric epsilon or near-integer snapping.\n\nLimitation: Nonzero inputs and published numeric fields must be finite normal binary64; NUMERIC_RANGE requires translation/rescaling. Mathematical zero is retained, never a clamp.\n\nLimitation: Coincident defining points reject INVALID_INPUT for slope and all line operations; distance zero and midpoint remain valid. Vertical slope/intercept are null.\n\nLimitation: Line coefficients use exact integer gcd only for exact safe integers; otherwise a common power-of-two normalization and canonical sign. Standard equations are floating presentations, not exact symbolic identities.\n\nLimitation: Intersections of infinite lines (not segments): parallel distinct => empty, coincident => coincident, each with x/y null; other intersections return one point.\n\nLimitation: Undirected principal line angle is atan2(abs cross, abs dot) in [0,90] degrees. Exact predicates determine status; a non-perpendicular angle can round to90 degrees.\n\nLimitation: Full binary64 output without near-zero clamping. Typical well-conditioned scalar error budget relative2e-12; ill-conditioned inputs require their own sensitivity analysis. No positional bound is claimed for perturbed inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/line-equation": { "post": { "operationId": "calculate_math_geometry_coordinate_alias_line_equation", "summary": "Coordinate geometry (line-equation page alias)", "description": "Distance, midpoint, slope, two-point line, point-line distance, line intersection, and angle in the plane. Slope is not share-key m. Discovery /line-equation, /point-line-distance, /line-intersection, /angle-between-lines. Not Pythagorean, not CAS. (calculation_version 1.8.0)\n\nSemantic capability: `math.geometry.coordinate`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cartesian R²; all coordinates use one consistent length unit; angle outputs include radians and degrees.\n\nLimitation: Strict decimal inputs; matching x0/px and y0/py aliases; unknown fields reject. Omitted mode defaults distance. Discovery entry URLs lock their documented operation.\n\nLimitation: Exact dyadic predicates classify the supplied normalized binary64 values; decimal-to-binary rounding still affects nearly parallel lines and input-sensitive intersections. No absolute geometric epsilon or near-integer snapping.\n\nLimitation: Nonzero inputs and published numeric fields must be finite normal binary64; NUMERIC_RANGE requires translation/rescaling. Mathematical zero is retained, never a clamp.\n\nLimitation: Coincident defining points reject INVALID_INPUT for slope and all line operations; distance zero and midpoint remain valid. Vertical slope/intercept are null.\n\nLimitation: Line coefficients use exact integer gcd only for exact safe integers; otherwise a common power-of-two normalization and canonical sign. Standard equations are floating presentations, not exact symbolic identities.\n\nLimitation: Intersections of infinite lines (not segments): parallel distinct => empty, coincident => coincident, each with x/y null; other intersections return one point.\n\nLimitation: Undirected principal line angle is atan2(abs cross, abs dot) in [0,90] degrees. Exact predicates determine status; a non-perpendicular angle can round to90 degrees.\n\nLimitation: Full binary64 output without near-zero clamping. Typical well-conditioned scalar error budget relative2e-12; ill-conditioned inputs require their own sensitivity analysis. No positional bound is claimed for perturbed inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/point-line-distance": { "post": { "operationId": "calculate_math_geometry_coordinate_alias_point_line_distance", "summary": "Coordinate geometry (point-line-distance page alias)", "description": "Distance, midpoint, slope, two-point line, point-line distance, line intersection, and angle in the plane. Slope is not share-key m. Discovery /line-equation, /point-line-distance, /line-intersection, /angle-between-lines. Not Pythagorean, not CAS. (calculation_version 1.8.0)\n\nSemantic capability: `math.geometry.coordinate`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cartesian R²; all coordinates use one consistent length unit; angle outputs include radians and degrees.\n\nLimitation: Strict decimal inputs; matching x0/px and y0/py aliases; unknown fields reject. Omitted mode defaults distance. Discovery entry URLs lock their documented operation.\n\nLimitation: Exact dyadic predicates classify the supplied normalized binary64 values; decimal-to-binary rounding still affects nearly parallel lines and input-sensitive intersections. No absolute geometric epsilon or near-integer snapping.\n\nLimitation: Nonzero inputs and published numeric fields must be finite normal binary64; NUMERIC_RANGE requires translation/rescaling. Mathematical zero is retained, never a clamp.\n\nLimitation: Coincident defining points reject INVALID_INPUT for slope and all line operations; distance zero and midpoint remain valid. Vertical slope/intercept are null.\n\nLimitation: Line coefficients use exact integer gcd only for exact safe integers; otherwise a common power-of-two normalization and canonical sign. Standard equations are floating presentations, not exact symbolic identities.\n\nLimitation: Intersections of infinite lines (not segments): parallel distinct => empty, coincident => coincident, each with x/y null; other intersections return one point.\n\nLimitation: Undirected principal line angle is atan2(abs cross, abs dot) in [0,90] degrees. Exact predicates determine status; a non-perpendicular angle can round to90 degrees.\n\nLimitation: Full binary64 output without near-zero clamping. Typical well-conditioned scalar error budget relative2e-12; ill-conditioned inputs require their own sensitivity analysis. No positional bound is claimed for perturbed inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/line-intersection": { "post": { "operationId": "calculate_math_geometry_coordinate_alias_line_intersection", "summary": "Coordinate geometry (line-intersection page alias)", "description": "Distance, midpoint, slope, two-point line, point-line distance, line intersection, and angle in the plane. Slope is not share-key m. Discovery /line-equation, /point-line-distance, /line-intersection, /angle-between-lines. Not Pythagorean, not CAS. (calculation_version 1.8.0)\n\nSemantic capability: `math.geometry.coordinate`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cartesian R²; all coordinates use one consistent length unit; angle outputs include radians and degrees.\n\nLimitation: Strict decimal inputs; matching x0/px and y0/py aliases; unknown fields reject. Omitted mode defaults distance. Discovery entry URLs lock their documented operation.\n\nLimitation: Exact dyadic predicates classify the supplied normalized binary64 values; decimal-to-binary rounding still affects nearly parallel lines and input-sensitive intersections. No absolute geometric epsilon or near-integer snapping.\n\nLimitation: Nonzero inputs and published numeric fields must be finite normal binary64; NUMERIC_RANGE requires translation/rescaling. Mathematical zero is retained, never a clamp.\n\nLimitation: Coincident defining points reject INVALID_INPUT for slope and all line operations; distance zero and midpoint remain valid. Vertical slope/intercept are null.\n\nLimitation: Line coefficients use exact integer gcd only for exact safe integers; otherwise a common power-of-two normalization and canonical sign. Standard equations are floating presentations, not exact symbolic identities.\n\nLimitation: Intersections of infinite lines (not segments): parallel distinct => empty, coincident => coincident, each with x/y null; other intersections return one point.\n\nLimitation: Undirected principal line angle is atan2(abs cross, abs dot) in [0,90] degrees. Exact predicates determine status; a non-perpendicular angle can round to90 degrees.\n\nLimitation: Full binary64 output without near-zero clamping. Typical well-conditioned scalar error budget relative2e-12; ill-conditioned inputs require their own sensitivity analysis. No positional bound is claimed for perturbed inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/angle-between-lines": { "post": { "operationId": "calculate_math_geometry_coordinate_alias_angle_between_lines", "summary": "Coordinate geometry (angle-between-lines page alias)", "description": "Distance, midpoint, slope, two-point line, point-line distance, line intersection, and angle in the plane. Slope is not share-key m. Discovery /line-equation, /point-line-distance, /line-intersection, /angle-between-lines. Not Pythagorean, not CAS. (calculation_version 1.8.0)\n\nSemantic capability: `math.geometry.coordinate`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Cartesian R²; all coordinates use one consistent length unit; angle outputs include radians and degrees.\n\nLimitation: Strict decimal inputs; matching x0/px and y0/py aliases; unknown fields reject. Omitted mode defaults distance. Discovery entry URLs lock their documented operation.\n\nLimitation: Exact dyadic predicates classify the supplied normalized binary64 values; decimal-to-binary rounding still affects nearly parallel lines and input-sensitive intersections. No absolute geometric epsilon or near-integer snapping.\n\nLimitation: Nonzero inputs and published numeric fields must be finite normal binary64; NUMERIC_RANGE requires translation/rescaling. Mathematical zero is retained, never a clamp.\n\nLimitation: Coincident defining points reject INVALID_INPUT for slope and all line operations; distance zero and midpoint remain valid. Vertical slope/intercept are null.\n\nLimitation: Line coefficients use exact integer gcd only for exact safe integers; otherwise a common power-of-two normalization and canonical sign. Standard equations are floating presentations, not exact symbolic identities.\n\nLimitation: Intersections of infinite lines (not segments): parallel distinct => empty, coincident => coincident, each with x/y null; other intersections return one point.\n\nLimitation: Undirected principal line angle is atan2(abs cross, abs dot) in [0,90] degrees. Exact predicates determine status; a non-perpendicular angle can round to90 degrees.\n\nLimitation: Full binary64 output without near-zero clamping. Typical well-conditioned scalar error budget relative2e-12; ill-conditioned inputs require their own sensitivity analysis. No positional bound is claimed for perturbed inputs.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.geometry.coordinate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector": { "post": { "operationId": "calculate_math_vector", "summary": "Vector", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector-magnitude": { "post": { "operationId": "calculate_math_vector_alias_vector_magnitude", "summary": "Vector (vector-magnitude page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector-normalize": { "post": { "operationId": "calculate_math_vector_alias_vector_normalize", "summary": "Vector (vector-normalize page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector-add": { "post": { "operationId": "calculate_math_vector_alias_vector_add", "summary": "Vector (vector-add page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector-sub": { "post": { "operationId": "calculate_math_vector_alias_vector_sub", "summary": "Vector (vector-sub page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/dot-product": { "post": { "operationId": "calculate_math_vector_alias_dot_product", "summary": "Vector (dot-product page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/cross-product": { "post": { "operationId": "calculate_math_vector_alias_cross_product", "summary": "Vector (cross-product page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector-angle": { "post": { "operationId": "calculate_math_vector_alias_vector_angle", "summary": "Vector (vector-angle page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector-projection": { "post": { "operationId": "calculate_math_vector_alias_vector_projection", "summary": "Vector (vector-projection page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/vector-triple": { "post": { "operationId": "calculate_math_vector_alias_vector_triple", "summary": "Vector (vector-triple page alias)", "description": "R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries. (calculation_version 1.8.0)\n\nSemantic capability: `math.vector`.\n\nCalculation version: `1.8.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.\n\nLimitation: Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.\n\nLimitation: Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.\n\nLimitation: Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.\n\nLimitation: Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.\n\nLimitation: Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.\n\nLimitation: Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.\n\nLimitation: Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.8.0" ] }, "description": "Pin calculation_version (published: 1.8.0); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.vector.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.8.0", "examples": [ "1.8.0" ] } } }, "example": { "inputs": {}, "calculation_version": "1.8.0" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.vector.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/solid-geometry": { "post": { "operationId": "calculate_math_geometry_solid", "summary": "Solid geometry", "description": "Volume, surface and secondary dimensions for20 Euclidean solid models. Strict decimal inputs, one consistent length unit, binary64 normal-range outputs, bounded figures; ellipsoid surface uses spheroid forms or incomplete elliptic integrals. (calculation_version 1.19.0)\n\nSemantic capability: `math.geometry.solid`.\n\nCalculation version: `1.19.0`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Right solids only; not oblique\n\nLimitation: Not the circle-only page — 2-D circle stays on math.geometry.circle\n\nLimitation: Not a vector — math.vector is R²/R³ algebra\n\nLimitation: Not ISO 5167-5 cone meter (physics.fluid.iso_cone)\n\nLimitation: Torus is a ring torus: major R > tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0 tube r; horn/spindle out of scope\n\nLimitation: Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page\n\nLimitation: Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page\n\nLimitation: Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page\n\nLimitation: Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page\n\nLimitation: Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page\n\nLimitation: Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page\n\nLimitation: Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page\n\nLimitation: Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid\n\nLimitation: Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum\n\nLimitation: Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid\n\nLimitation: Ellipsoid needs a,b,c>0; V=4/3 πabc; surface is the exact elliptic-integral / spheroid model numerically evaluated (modulus k, not m=k²); axes sorted internally; a=b=c is a sphere; not /sphere; not the 2-D ellipse\n\nLimitation: Spherical cap needs r>0 and 00; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge\n\nLimitation: Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune\n\nLimitation: Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector\n\nLimitation: Spherical sector needs r>0 and 0r>0; parallelogram0r>0; parallelogram0r>0; parallelogram0r>0; parallelogram0r>0; parallelogram0r>0; parallelogram0r>0; parallelogram0r>0; parallelogram00 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/error-function": { "post": { "operationId": "calculate_math_special_alias_error_function", "summary": "Special functions (error-function page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gamma-function": { "post": { "operationId": "calculate_math_special_alias_gamma_function", "summary": "Special functions (gamma-function page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/bessel-function": { "post": { "operationId": "calculate_math_special_alias_bessel_function", "summary": "Special functions (bessel-function page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/lambert-w": { "post": { "operationId": "calculate_math_special_alias_lambert_w", "summary": "Special functions (lambert-w page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/lambert-w-minus-1": { "post": { "operationId": "calculate_math_special_alias_lambert_w_minus_1", "summary": "Special functions (lambert-w-minus-1 page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/beta-function": { "post": { "operationId": "calculate_math_special_alias_beta_function", "summary": "Special functions (beta-function page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/incomplete-beta": { "post": { "operationId": "calculate_math_special_alias_incomplete_beta", "summary": "Special functions (incomplete-beta page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/sinc-function": { "post": { "operationId": "calculate_math_special_alias_sinc_function", "summary": "Special functions (sinc-function page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/normalized-sinc": { "post": { "operationId": "calculate_math_special_alias_normalized_sinc", "summary": "Special functions (normalized-sinc page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/bessel-y": { "post": { "operationId": "calculate_math_special_alias_bessel_y", "summary": "Special functions (bessel-y page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/bessel-i": { "post": { "operationId": "calculate_math_special_alias_bessel_i", "summary": "Special functions (bessel-i page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/bessel-k": { "post": { "operationId": "calculate_math_special_alias_bessel_k", "summary": "Special functions (bessel-k page alias)", "description": "Real erf, erfc, Gamma, log-gamma, integer-order J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta B(x,y), incomplete beta B_x(a,b), unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial, not CAS. (calculation_version 1.10.6)\n\nSemantic capability: `math.special`.\n\nCalculation version: `1.10.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Real, dimensionless binary64 inputs; publishes12 significant digits, no arbitrary-precision/exact claim.\n\nLimitation: Default mode erf and Bessel order0 apply only when absent; explicit empty/null rejects. All supplied numeric aliases must agree; known irrelevant numeric parameters are parsed then ignored.\n\nLimitation: Gamma poles reject. Nonzero Gamma that underflows rejects NUMERICAL_RANGE_ERROR; positive overflow suggests lgamma. lgamma is computed directly for x>0 with a stable Taylor expansion near1 and2.\n\nLimitation: Bessel integer n0–8, |x|≤80, Y/K require x>0; subnormal error and zeros limit relative accuracy.\n\nLimitation: Lambert W0 and W-1 explicit real branches; binary64 -1/e designated endpoint, no tolerance band absorbs adjacent inputs.\n\nLimitation: Beta shapes positive and at most1e6, except exact B(x,1)=1/x or B(1,y)=1/y. Incomplete beta shapes at most1e6. CF capped10000 steps; failure NO_CONVERGENCE.\n\nLimitation: erf/erfc and beta tails can round to zero only on binary64 underflow, not an absolute display cutoff. Regularized incomplete beta evaluated separately in logs.\n\nLimitation: Normalized sinc uses sinpi reduction and returns zero at representable nonzero integer x. Other tiny nonzero results retain significance.\n\nLimitation: Numeric references have relative1e-10, with J/Y near zeros absolute2e-14,4 minimum subnormals otherwise. No global error proof for all real inputs.\n\nLimitation: Browser interaction computes locally; parameterized share pages, REST and MCP send inputs to server. Logs/retention/region are deployment concerns; no zero-log promise.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.10.6" ] }, "description": "Pin calculation_version (published: 1.10.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.special.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.10.6", "examples": [ "1.10.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.10.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.special.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/discrete-fourier-transform": { "post": { "operationId": "calculate_math_transform_dft", "summary": "Discrete Fourier transform", "description": "Direct DFT / IDFT and radix-2 FFT / IFFT of a length-N sequence, N≤64. FFT requires N=2^k. Numpy backward: unnormalized forward, 1/N inverse. Discovery /dft, /inverse-dft, /fft, /ifft. Not Laplace, not Z, not CAS. (calculation_version 1.2.3)\n\nSemantic capability: `math.transform.dft`.\n\nCalculation version: `1.2.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Direct O(N²) DFT/IDFT, N≤64; radix-2 FFT/IFFT, N=2^k ≤64\n\nLimitation: Numpy backward: unnormalized forward, 1/N inverse\n\nLimitation: FFT agrees with DFT for power-of-2 N (Float64)\n\nLimitation: Not Laplace / Z — other canonicals\n\nLimitation: Not CAS\n\nLimitation: unknown mode (including laplace, cas) → INVALID_MODE\n\nLimitation: Decimal nonzero input underflow → NUMERIC_UNDERFLOW; malformed/conflicting inputs rejected.\n\nLimitation: Exact dyadic sums/products of binary64 twiddles; no exact transcendental or per-bin relative guarantee near cancellation zeros.\n\nLimitation: Nonzero evaluated output component below binary64 or nonfinite output/magnitude → NUMERICAL_RANGE_ERROR. Intermediate overflow is avoided. Input echoes retain binary64; outputs publish12 significant digits.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.3" ] }, "description": "Pin calculation_version (published: 1.2.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.3", "examples": [ "1.2.3" ] } } }, "example": { "inputs": { "mode": "fft", "samples": [ 1, 0, 0, 0 ] }, "calculation_version": "1.2.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/dft": { "post": { "operationId": "calculate_math_transform_dft_alias_dft", "summary": "Discrete Fourier transform (dft page alias)", "description": "Direct DFT / IDFT and radix-2 FFT / IFFT of a length-N sequence, N≤64. FFT requires N=2^k. Numpy backward: unnormalized forward, 1/N inverse. Discovery /dft, /inverse-dft, /fft, /ifft. Not Laplace, not Z, not CAS. (calculation_version 1.2.3)\n\nSemantic capability: `math.transform.dft`.\n\nCalculation version: `1.2.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Direct O(N²) DFT/IDFT, N≤64; radix-2 FFT/IFFT, N=2^k ≤64\n\nLimitation: Numpy backward: unnormalized forward, 1/N inverse\n\nLimitation: FFT agrees with DFT for power-of-2 N (Float64)\n\nLimitation: Not Laplace / Z — other canonicals\n\nLimitation: Not CAS\n\nLimitation: unknown mode (including laplace, cas) → INVALID_MODE\n\nLimitation: Decimal nonzero input underflow → NUMERIC_UNDERFLOW; malformed/conflicting inputs rejected.\n\nLimitation: Exact dyadic sums/products of binary64 twiddles; no exact transcendental or per-bin relative guarantee near cancellation zeros.\n\nLimitation: Nonzero evaluated output component below binary64 or nonfinite output/magnitude → NUMERICAL_RANGE_ERROR. Intermediate overflow is avoided. Input echoes retain binary64; outputs publish12 significant digits.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.3" ] }, "description": "Pin calculation_version (published: 1.2.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.3", "examples": [ "1.2.3" ] } } }, "example": { "inputs": { "mode": "fft", "samples": [ 1, 0, 0, 0 ] }, "calculation_version": "1.2.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/inverse-dft": { "post": { "operationId": "calculate_math_transform_dft_alias_inverse_dft", "summary": "Discrete Fourier transform (inverse-dft page alias)", "description": "Direct DFT / IDFT and radix-2 FFT / IFFT of a length-N sequence, N≤64. FFT requires N=2^k. Numpy backward: unnormalized forward, 1/N inverse. Discovery /dft, /inverse-dft, /fft, /ifft. Not Laplace, not Z, not CAS. (calculation_version 1.2.3)\n\nSemantic capability: `math.transform.dft`.\n\nCalculation version: `1.2.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Direct O(N²) DFT/IDFT, N≤64; radix-2 FFT/IFFT, N=2^k ≤64\n\nLimitation: Numpy backward: unnormalized forward, 1/N inverse\n\nLimitation: FFT agrees with DFT for power-of-2 N (Float64)\n\nLimitation: Not Laplace / Z — other canonicals\n\nLimitation: Not CAS\n\nLimitation: unknown mode (including laplace, cas) → INVALID_MODE\n\nLimitation: Decimal nonzero input underflow → NUMERIC_UNDERFLOW; malformed/conflicting inputs rejected.\n\nLimitation: Exact dyadic sums/products of binary64 twiddles; no exact transcendental or per-bin relative guarantee near cancellation zeros.\n\nLimitation: Nonzero evaluated output component below binary64 or nonfinite output/magnitude → NUMERICAL_RANGE_ERROR. Intermediate overflow is avoided. Input echoes retain binary64; outputs publish12 significant digits.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.3" ] }, "description": "Pin calculation_version (published: 1.2.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.3", "examples": [ "1.2.3" ] } } }, "example": { "inputs": { "mode": "fft", "samples": [ 1, 0, 0, 0 ] }, "calculation_version": "1.2.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/fft": { "post": { "operationId": "calculate_math_transform_dft_alias_fft", "summary": "Discrete Fourier transform (fft page alias)", "description": "Direct DFT / IDFT and radix-2 FFT / IFFT of a length-N sequence, N≤64. FFT requires N=2^k. Numpy backward: unnormalized forward, 1/N inverse. Discovery /dft, /inverse-dft, /fft, /ifft. Not Laplace, not Z, not CAS. (calculation_version 1.2.3)\n\nSemantic capability: `math.transform.dft`.\n\nCalculation version: `1.2.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Direct O(N²) DFT/IDFT, N≤64; radix-2 FFT/IFFT, N=2^k ≤64\n\nLimitation: Numpy backward: unnormalized forward, 1/N inverse\n\nLimitation: FFT agrees with DFT for power-of-2 N (Float64)\n\nLimitation: Not Laplace / Z — other canonicals\n\nLimitation: Not CAS\n\nLimitation: unknown mode (including laplace, cas) → INVALID_MODE\n\nLimitation: Decimal nonzero input underflow → NUMERIC_UNDERFLOW; malformed/conflicting inputs rejected.\n\nLimitation: Exact dyadic sums/products of binary64 twiddles; no exact transcendental or per-bin relative guarantee near cancellation zeros.\n\nLimitation: Nonzero evaluated output component below binary64 or nonfinite output/magnitude → NUMERICAL_RANGE_ERROR. Intermediate overflow is avoided. Input echoes retain binary64; outputs publish12 significant digits.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.3" ] }, "description": "Pin calculation_version (published: 1.2.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.3", "examples": [ "1.2.3" ] } } }, "example": { "inputs": { "mode": "fft", "samples": [ 1, 0, 0, 0 ] }, "calculation_version": "1.2.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/ifft": { "post": { "operationId": "calculate_math_transform_dft_alias_ifft", "summary": "Discrete Fourier transform (ifft page alias)", "description": "Direct DFT / IDFT and radix-2 FFT / IFFT of a length-N sequence, N≤64. FFT requires N=2^k. Numpy backward: unnormalized forward, 1/N inverse. Discovery /dft, /inverse-dft, /fft, /ifft. Not Laplace, not Z, not CAS. (calculation_version 1.2.3)\n\nSemantic capability: `math.transform.dft`.\n\nCalculation version: `1.2.3`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Direct O(N²) DFT/IDFT, N≤64; radix-2 FFT/IFFT, N=2^k ≤64\n\nLimitation: Numpy backward: unnormalized forward, 1/N inverse\n\nLimitation: FFT agrees with DFT for power-of-2 N (Float64)\n\nLimitation: Not Laplace / Z — other canonicals\n\nLimitation: Not CAS\n\nLimitation: unknown mode (including laplace, cas) → INVALID_MODE\n\nLimitation: Decimal nonzero input underflow → NUMERIC_UNDERFLOW; malformed/conflicting inputs rejected.\n\nLimitation: Exact dyadic sums/products of binary64 twiddles; no exact transcendental or per-bin relative guarantee near cancellation zeros.\n\nLimitation: Nonzero evaluated output component below binary64 or nonfinite output/magnitude → NUMERICAL_RANGE_ERROR. Intermediate overflow is avoided. Input echoes retain binary64; outputs publish12 significant digits.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.2.3" ] }, "description": "Pin calculation_version (published: 1.2.3); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.2.3", "examples": [ "1.2.3" ] } } }, "example": { "inputs": { "mode": "fft", "samples": [ 1, 0, 0, 0 ] }, "calculation_version": "1.2.3" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.dft.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/laplace-transform": { "post": { "operationId": "calculate_math_transform_laplace", "summary": "Laplace transform", "description": "Unilateral Laplace table of causal elementary pairs: exp, sin, cos, step, ramp, t^n, damped sin/cos. Evaluate F(s) or f(t). Discovery /inverse-laplace. Not DFT, not Z, not Bromwich, not CAS. (calculation_version 1.0.4)\n\nSemantic capability: `math.transform.laplace`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Unilateral causal elementary table; eight named pairs, power integer0–8; inverse table evaluation at t≥0, step(0)=1 and0^0=1 convention\n\nLimitation: Finite real s strictly inside the conservative stated ROC, even degenerate zero sine; real dimensionless parameters, omega in radians per unit t\n\nLimitation: Binary64 approximate evaluation,12 significant digits;2e-11 relative fixture tolerance, no uniform accuracy theorem; conditioned near poles/trig zeros\n\nLimitation: Coded input underflow, numerical range/phase/quantization refusal; no fabricated nonzero-to-zero success\n\nLimitation: Inputs/method/pair aliases must agree; unknown fields rejected\n\nLimitation: DFT, Z and unrestricted symbolic/contour inversion are separate models", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.laplace.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": { "mode": "laplace", "f": "exp", "a": -1, "s": 1 }, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.laplace.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/inverse-laplace": { "post": { "operationId": "calculate_math_transform_laplace_alias_inverse_laplace", "summary": "Laplace transform (inverse-laplace page alias)", "description": "Unilateral Laplace table of causal elementary pairs: exp, sin, cos, step, ramp, t^n, damped sin/cos. Evaluate F(s) or f(t). Discovery /inverse-laplace. Not DFT, not Z, not Bromwich, not CAS. (calculation_version 1.0.4)\n\nSemantic capability: `math.transform.laplace`.\n\nCalculation version: `1.0.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Unilateral causal elementary table; eight named pairs, power integer0–8; inverse table evaluation at t≥0, step(0)=1 and0^0=1 convention\n\nLimitation: Finite real s strictly inside the conservative stated ROC, even degenerate zero sine; real dimensionless parameters, omega in radians per unit t\n\nLimitation: Binary64 approximate evaluation,12 significant digits;2e-11 relative fixture tolerance, no uniform accuracy theorem; conditioned near poles/trig zeros\n\nLimitation: Coded input underflow, numerical range/phase/quantization refusal; no fabricated nonzero-to-zero success\n\nLimitation: Inputs/method/pair aliases must agree; unknown fields rejected\n\nLimitation: DFT, Z and unrestricted symbolic/contour inversion are separate models", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.4" ] }, "description": "Pin calculation_version (published: 1.0.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.laplace.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.4", "examples": [ "1.0.4" ] } } }, "example": { "inputs": { "mode": "laplace", "f": "exp", "a": -1, "s": 1 }, "calculation_version": "1.0.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.laplace.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/z-transform": { "post": { "operationId": "calculate_math_transform_z", "summary": "Z transform", "description": "Unilateral Z table of causal elementary pairs: a^n, step, ramp, n a^n, sin, cos, damped sin/cos. Evaluate X(z) or x[n]. Discovery /inverse-z. Not DFT, not Laplace, not residue, not CAS. (calculation_version 1.0.5)\n\nSemantic capability: `math.transform.z`.\n\nCalculation version: `1.0.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Unilateral causal elementary table; eight named pairs, inverse integer0–64; u[0]=1,a^0=1 including a=0\n\nLimitation: Finite real z strictly outside conservative ROC radius on either real branch, including degenerate zero sine; a,z dimensionless, omega radians per sample\n\nLimitation: Binary64 approximate evaluation,12 significant digits;2e-11 relative fixture tolerance, no uniform accuracy theorem; conditioned near poles and trig zeros\n\nLimitation: Coded decimal input underflow and numerical range/phase/quantization refusals; inverse subnormal relative precision may be refused despite representability\n\nLimitation: Aliases must agree; null, nondecimal scalar forms and unknown fields rejected; inverse URL locks mode\n\nLimitation: Arbitrary symbolic sequence and contour/residue inversion are outside this named table", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.5" ] }, "description": "Pin calculation_version (published: 1.0.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.z.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.5", "examples": [ "1.0.5" ] } } }, "example": { "inputs": { "mode": "z", "f": "geom", "a": 0.5, "z": 1 }, "calculation_version": "1.0.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.z.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/inverse-z": { "post": { "operationId": "calculate_math_transform_z_alias_inverse_z", "summary": "Z transform (inverse-z page alias)", "description": "Unilateral Z table of causal elementary pairs: a^n, step, ramp, n a^n, sin, cos, damped sin/cos. Evaluate X(z) or x[n]. Discovery /inverse-z. Not DFT, not Laplace, not residue, not CAS. (calculation_version 1.0.5)\n\nSemantic capability: `math.transform.z`.\n\nCalculation version: `1.0.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Unilateral causal elementary table; eight named pairs, inverse integer0–64; u[0]=1,a^0=1 including a=0\n\nLimitation: Finite real z strictly outside conservative ROC radius on either real branch, including degenerate zero sine; a,z dimensionless, omega radians per sample\n\nLimitation: Binary64 approximate evaluation,12 significant digits;2e-11 relative fixture tolerance, no uniform accuracy theorem; conditioned near poles and trig zeros\n\nLimitation: Coded decimal input underflow and numerical range/phase/quantization refusals; inverse subnormal relative precision may be refused despite representability\n\nLimitation: Aliases must agree; null, nondecimal scalar forms and unknown fields rejected; inverse URL locks mode\n\nLimitation: Arbitrary symbolic sequence and contour/residue inversion are outside this named table", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.0.5" ] }, "description": "Pin calculation_version (published: 1.0.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.transform.z.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.0.5", "examples": [ "1.0.5" ] } } }, "example": { "inputs": { "mode": "z", "f": "geom", "a": 0.5, "z": 1 }, "calculation_version": "1.0.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.transform.z.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/linear-system": { "post": { "operationId": "calculate_math_linear_algebra", "summary": "Linear system / small matrix", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-determinant": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_determinant", "summary": "Linear system / small matrix (matrix-determinant page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-inverse": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_inverse", "summary": "Linear system / small matrix (matrix-inverse page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-rank": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_rank", "summary": "Linear system / small matrix (matrix-rank page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-eigenvalues": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_eigenvalues", "summary": "Linear system / small matrix (matrix-eigenvalues page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-lu": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_lu", "summary": "Linear system / small matrix (matrix-lu page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-cholesky": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_cholesky", "summary": "Linear system / small matrix (matrix-cholesky page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-qr": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_qr", "summary": "Linear system / small matrix (matrix-qr page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-svd": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_svd", "summary": "Linear system / small matrix (matrix-svd page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. 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Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/least-squares": { "post": { "operationId": "calculate_math_linear_algebra_alias_least_squares", "summary": "Linear system / small matrix (least-squares page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/matrix-rref": { "post": { "operationId": "calculate_math_linear_algebra_alias_matrix_rref", "summary": "Linear system / small matrix (matrix-rref page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/condition-number": { "post": { "operationId": "calculate_math_linear_algebra_alias_condition_number", "summary": "Linear system / small matrix (condition-number page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/nullspace": { "post": { "operationId": "calculate_math_linear_algebra_alias_nullspace", "summary": "Linear system / small matrix (nullspace page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/column-space": { "post": { "operationId": "calculate_math_linear_algebra_alias_column_space", "summary": "Linear system / small matrix (column-space page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/row-space": { "post": { "operationId": "calculate_math_linear_algebra_alias_row_space", "summary": "Linear system / small matrix (row-space page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/left-nullspace": { "post": { "operationId": "calculate_math_linear_algebra_alias_left_nullspace", "summary": "Linear system / small matrix (left-nullspace page alias)", "description": "Solve Ax=b for order 2–4, plus det, inverse, rank, LU, Cholesky (SPD A=LLᵀ), QR and SVD (square or rectangular m×n with m,n∈[2,4]), least squares (same rectangular shape), RREF, condition number, nullspace, column space, rowspace, left-nullspace, eigen, multiply, transpose. Same engine as /workspace/matrix. Discovery pages share this capability. Not a CAS. Not Statistics regression. (calculation_version 1.14.16)\n\nSemantic capability: `math.linear_algebra`.\n\nCalculation version: `1.14.16`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Order ≤ 4 (local small-matrix seed)\n\nLimitation: Singular inverse → SINGULAR_MATRIX\n\nLimitation: qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square\n\nLimitation: Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)\n\nLimitation: Not Statistics regression / large-matrix server compute\n\nLimitation: Not 2-norm κ₂ as a product / CAS / Jordan form\n\nLimitation: Finite decimal scalars only; nonzero text underflow is rejected. Conflicting aliases or nested/flat values are rejected. Every required cell must be supplied.\n\nLimitation: Numerical outputs that exceed binary64 range or cannot be resolved at working precision refuse with NUMERIC_PRECISION_LIMIT; out-of-range auxiliary determinants are omitted with a warning.\n\nLimitation: Singular solve distinguishes consistent (infinite) from inconsistent systems using the stated numerical rank tolerance.\n\nLimitation: Cholesky: relative pairwise symmetry tolerance 1e-12, with no absolute floor; accepted differences mirror the lower triangle into effective_A and emit symmetry_adjusted. A preserves the original inputs.\n\nLimitation: Cholesky: exact binary64 leading-minor signs distinguish NOT_POSITIVE_DEFINITE from NUMERIC_PRECISION_LIMIT. Positive pivots are not rejected merely for being small.\n\nLimitation: Cholesky: L and A preserve binary64 round-trip values. Residuals use published L versus original A; relative Frobenius residual uses common scaling. Absolute residual can underflow to zero. Condition estimate is 1-norm; ill_conditioned threshold is 1e8.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.14.16" ] }, "description": "Pin calculation_version (published: 1.14.16); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.14.16", "examples": [ "1.14.16" ] } } }, "example": { "inputs": {}, "calculation_version": "1.14.16" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.linear_algebra.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/numerical-root": { "post": { "operationId": "calculate_math_numerical_root", "summary": "Numerical root", "description": "Newton, bisection, or secant for an approximate real zero of a polynomial or sin. exp has no finite real zero and returns NO_CONVERGENCE. Discovery /nonlinear-equation. Not the nth-root page, not CAS, not a system. (calculation_version 1.1.6)\n\nSemantic capability: `math.numerical.root`.\n\nCalculation version: `1.1.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not ⁿ√a — that remains /calc/math/root\n\nLimitation: Not three independent Newton/bisection/secant product pages\n\nLimitation: Not CAS / not a nonlinear system\n\nLimitation: Degree > 8 → INVALID_INPUT\n\nLimitation: No convergence → NO_CONVERGENCE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.6" ] }, "description": "Pin calculation_version (published: 1.1.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.root.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.6", "examples": [ "1.1.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.root.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/nonlinear-equation": { "post": { "operationId": "calculate_math_numerical_root_alias_nonlinear_equation", "summary": "Numerical root (nonlinear-equation page alias)", "description": "Newton, bisection, or secant for an approximate real zero of a polynomial or sin. exp has no finite real zero and returns NO_CONVERGENCE. Discovery /nonlinear-equation. Not the nth-root page, not CAS, not a system. (calculation_version 1.1.6)\n\nSemantic capability: `math.numerical.root`.\n\nCalculation version: `1.1.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not ⁿ√a — that remains /calc/math/root\n\nLimitation: Not three independent Newton/bisection/secant product pages\n\nLimitation: Not CAS / not a nonlinear system\n\nLimitation: Degree > 8 → INVALID_INPUT\n\nLimitation: No convergence → NO_CONVERGENCE", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.6" ] }, "description": "Pin calculation_version (published: 1.1.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.root.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.6", "examples": [ "1.1.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.root.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/definite-integral": { "post": { "operationId": "calculate_math_numerical_definite_integral", "summary": "Definite integral", "description": "Composite trapezoid, Simpson 1/3, or Gauss–Legendre of a polynomial, sin, or exp on [a, b]. Not indefinite symbolic integrate. (calculation_version 1.1.5)\n\nSemantic capability: `math.numerical.definite_integral`.\n\nCalculation version: `1.1.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not indefinite / symbolic CAS integrate\n\nLimitation: Simpson/trapezoid n panels 2–10000; Simpson n forced even\n\nLimitation: Gauss–Legendre n nodes 2–8\n\nLimitation: Polynomial degree ≤ 8\n\nLimitation: Decimal nonzero-to-zero inputs and unresolved nonzero outputs are rejected (NUMERIC_UNDERFLOW).\n\nLimitation: n must be an integer; odd Simpson n rounds up to the next even panel count.\n\nLimitation: Integrand sample overflow/underflow and severe quadrature cancellation are rejected; rescale or split the interval.\n\nLimitation: exact is a binary64 analytic baseline; abs_err is the signed raw quadrature-minus-baseline difference, not a certified bound.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.5" ] }, "description": "Pin calculation_version (published: 1.1.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.5", "examples": [ "1.1.5" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/simpson-rule": { "post": { "operationId": "calculate_math_numerical_definite_integral_alias_simpson_rule", "summary": "Definite integral (simpson-rule page alias)", "description": "Composite trapezoid, Simpson 1/3, or Gauss–Legendre of a polynomial, sin, or exp on [a, b]. Not indefinite symbolic integrate. (calculation_version 1.1.5)\n\nSemantic capability: `math.numerical.definite_integral`.\n\nCalculation version: `1.1.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not indefinite / symbolic CAS integrate\n\nLimitation: Simpson/trapezoid n panels 2–10000; Simpson n forced even\n\nLimitation: Gauss–Legendre n nodes 2–8\n\nLimitation: Polynomial degree ≤ 8\n\nLimitation: Decimal nonzero-to-zero inputs and unresolved nonzero outputs are rejected (NUMERIC_UNDERFLOW).\n\nLimitation: n must be an integer; odd Simpson n rounds up to the next even panel count.\n\nLimitation: Integrand sample overflow/underflow and severe quadrature cancellation are rejected; rescale or split the interval.\n\nLimitation: exact is a binary64 analytic baseline; abs_err is the signed raw quadrature-minus-baseline difference, not a certified bound.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.5" ] }, "description": "Pin calculation_version (published: 1.1.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.5", "examples": [ "1.1.5" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/trapezoidal-rule": { "post": { "operationId": "calculate_math_numerical_definite_integral_alias_trapezoidal_rule", "summary": "Definite integral (trapezoidal-rule page alias)", "description": "Composite trapezoid, Simpson 1/3, or Gauss–Legendre of a polynomial, sin, or exp on [a, b]. Not indefinite symbolic integrate. (calculation_version 1.1.5)\n\nSemantic capability: `math.numerical.definite_integral`.\n\nCalculation version: `1.1.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not indefinite / symbolic CAS integrate\n\nLimitation: Simpson/trapezoid n panels 2–10000; Simpson n forced even\n\nLimitation: Gauss–Legendre n nodes 2–8\n\nLimitation: Polynomial degree ≤ 8\n\nLimitation: Decimal nonzero-to-zero inputs and unresolved nonzero outputs are rejected (NUMERIC_UNDERFLOW).\n\nLimitation: n must be an integer; odd Simpson n rounds up to the next even panel count.\n\nLimitation: Integrand sample overflow/underflow and severe quadrature cancellation are rejected; rescale or split the interval.\n\nLimitation: exact is a binary64 analytic baseline; abs_err is the signed raw quadrature-minus-baseline difference, not a certified bound.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.5" ] }, "description": "Pin calculation_version (published: 1.1.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.5", "examples": [ "1.1.5" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/gauss-quadrature": { "post": { "operationId": "calculate_math_numerical_definite_integral_alias_gauss_quadrature", "summary": "Definite integral (gauss-quadrature page alias)", "description": "Composite trapezoid, Simpson 1/3, or Gauss–Legendre of a polynomial, sin, or exp on [a, b]. Not indefinite symbolic integrate. (calculation_version 1.1.5)\n\nSemantic capability: `math.numerical.definite_integral`.\n\nCalculation version: `1.1.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not indefinite / symbolic CAS integrate\n\nLimitation: Simpson/trapezoid n panels 2–10000; Simpson n forced even\n\nLimitation: Gauss–Legendre n nodes 2–8\n\nLimitation: Polynomial degree ≤ 8\n\nLimitation: Decimal nonzero-to-zero inputs and unresolved nonzero outputs are rejected (NUMERIC_UNDERFLOW).\n\nLimitation: n must be an integer; odd Simpson n rounds up to the next even panel count.\n\nLimitation: Integrand sample overflow/underflow and severe quadrature cancellation are rejected; rescale or split the interval.\n\nLimitation: exact is a binary64 analytic baseline; abs_err is the signed raw quadrature-minus-baseline difference, not a certified bound.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.5" ] }, "description": "Pin calculation_version (published: 1.1.5); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.5", "examples": [ "1.1.5" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.5" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.definite_integral.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/numerical-interpolation": { "post": { "operationId": "calculate_math_numerical_interpolate", "summary": "Numerical interpolation", "description": "Piecewise-linear, Lagrange, or natural cubic spline of tabulated (x, y). Not regression, not CAS. (calculation_version 1.1.6)\n\nSemantic capability: `math.numerical.interpolate`.\n\nCalculation version: `1.1.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not Akima, PCHIP, clamped spline, or statistical regression\n\nLimitation: Linear/spline x outside the table without extrapolate → VALUE_OUT_OF_RANGE\n\nLimitation: Lagrange limited to 9 points (degree ≤ 8); linear/spline table ≤ 100\n\nLimitation: Not a second interpolator and not CAS\n\nLimitation: Exact rational binary64-input primary evaluation; intermediate numerator/denominator at most16384 bits. Publication12 significant digits. Unrepresentable output, nonzero output underflow or unsupported spline coordinate normalization returns NUMERICAL_RANGE_ERROR.\n\nLimitation: Finite decimals only; full matching aliases and exactly two cells per node. Curve samples use illustrative binary64 arithmetic, not a certified error bound.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.6" ] }, "description": "Pin calculation_version (published: 1.1.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.interpolate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.6", "examples": [ "1.1.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.interpolate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/spline-interpolation": { "post": { "operationId": "calculate_math_numerical_interpolate_alias_spline_interpolation", "summary": "Numerical interpolation (spline-interpolation page alias)", "description": "Piecewise-linear, Lagrange, or natural cubic spline of tabulated (x, y). Not regression, not CAS. (calculation_version 1.1.6)\n\nSemantic capability: `math.numerical.interpolate`.\n\nCalculation version: `1.1.6`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not Akima, PCHIP, clamped spline, or statistical regression\n\nLimitation: Linear/spline x outside the table without extrapolate → VALUE_OUT_OF_RANGE\n\nLimitation: Lagrange limited to 9 points (degree ≤ 8); linear/spline table ≤ 100\n\nLimitation: Not a second interpolator and not CAS\n\nLimitation: Exact rational binary64-input primary evaluation; intermediate numerator/denominator at most16384 bits. Publication12 significant digits. Unrepresentable output, nonzero output underflow or unsupported spline coordinate normalization returns NUMERICAL_RANGE_ERROR.\n\nLimitation: Finite decimals only; full matching aliases and exactly two cells per node. Curve samples use illustrative binary64 arithmetic, not a certified error bound.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.6" ] }, "description": "Pin calculation_version (published: 1.1.6); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.interpolate.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.6", "examples": [ "1.1.6" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.6" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.interpolate.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/numerical-derivative": { "post": { "operationId": "calculate_math_numerical_derivative", "summary": "Numerical derivative", "description": "Forward, backward, or central finite difference of a polynomial, sin, or exp, plus a numeric two-sided limit. Discovery /two-sided-limit. Not symbolic d/dx. (calculation_version 1.1.4)\n\nSemantic capability: `math.numerical.derivative`.\n\nCalculation version: `1.1.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not symbolic / CAS d/dx\n\nLimitation: Not one-sided left/right; not L’Hôpital\n\nLimitation: h ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: Polynomial degree ≤ 8\n\nLimitation: Not a Statistics calculator\n\nLimitation: Strict decimal/scalar inputs; nonzero decimal and nonzero primary result underflow reject. Matching aliases required.\n\nLimitation: Finite-step value differs from analytic exact; abs_err is signed published value minus published baseline, not a certified bound.\n\nLimitation: For polynomial input, x±h denotes exact sums of supplied binary64 values, with exact dyadic intermediates.\n\nLimitation: Probe/gap/error diagnostics are rounded binary64 and may quantize to zero; no uniform relative accuracy claim at the subnormal scale.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.4" ] }, "description": "Pin calculation_version (published: 1.1.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.derivative.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.4", "examples": [ "1.1.4" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.derivative.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/two-sided-limit": { "post": { "operationId": "calculate_math_numerical_derivative_alias_two_sided_limit", "summary": "Numerical derivative (two-sided-limit page alias)", "description": "Forward, backward, or central finite difference of a polynomial, sin, or exp, plus a numeric two-sided limit. Discovery /two-sided-limit. Not symbolic d/dx. (calculation_version 1.1.4)\n\nSemantic capability: `math.numerical.derivative`.\n\nCalculation version: `1.1.4`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Not symbolic / CAS d/dx\n\nLimitation: Not one-sided left/right; not L’Hôpital\n\nLimitation: h ≤ 0 → VALUE_MUST_BE_POSITIVE\n\nLimitation: Polynomial degree ≤ 8\n\nLimitation: Not a Statistics calculator\n\nLimitation: Strict decimal/scalar inputs; nonzero decimal and nonzero primary result underflow reject. Matching aliases required.\n\nLimitation: Finite-step value differs from analytic exact; abs_err is signed published value minus published baseline, not a certified bound.\n\nLimitation: For polynomial input, x±h denotes exact sums of supplied binary64 values, with exact dyadic intermediates.\n\nLimitation: Probe/gap/error diagnostics are rounded binary64 and may quantize to zero; no uniform relative accuracy claim at the subnormal scale.", "tags": [ "CoreCapabilities" ], "parameters": [ { "name": "CalculatorX-Spec-Version", "in": "header", "required": false, "schema": { "type": "string", "examples": [ "1.1.4" ] }, "description": "Pin calculation_version (published: 1.1.4); mismatch returns 409" } ], "requestBody": { "required": true, "content": { "application/json": { "schema": { "type": "object", "required": [ "inputs" ], "properties": { "inputs": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.derivative.input.json" }, "calculation_version": { "type": "string", "description": "Optional pin; published version is 1.1.4", "examples": [ "1.1.4" ] } } }, "example": { "inputs": {}, "calculation_version": "1.1.4" } } } }, "responses": { "200": { "description": "Success", "content": { "application/json": { "schema": { "$ref": "https://www.calculatorx.com/schemas/math.numerical.derivative.output.json" } } } }, "400": { "description": "Invalid or incomplete inputs", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "404": { "description": "Unknown engine or capability", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "409": { "description": "VERSION_MISMATCH — pinned calculation_version unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "415": { "description": "Unsupported Content-Type (use application/json)", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "429": { "description": "RATE_LIMITED", "headers": { "Retry-After": { "description": "Seconds until the client may retry", "schema": { "type": "integer", "minimum": 1 } } }, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/RateLimitError" } } } }, "500": { "description": "Unexpected server error", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } }, "503": { "description": "Temporarily unavailable", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ApiError" } } } } } } }, "/api/v1/calc/one-dimensional-optimization": { "post": { "operationId": "calculate_math_numerical_optimize_1d", "summary": "One-dimensional optimization", "description": "Minimize a polynomial, sin, or exp on [a, b] by golden-section search or Brent. Not multivariate, not maximization, not CAS. (calculation_version 1.0.5)\n\nSemantic capability: `math.numerical.optimize_1d`.\n\nCalculation version: `1.0.5`.\n\nPin with body `calculation_version` or header `CalculatorX-Spec-Version`.\n\nLimitation: Minimize only; not multivariate, Nelder-Mead, gradient descent, maximization or CAS.\n\nLimitation: Unimodal assumption; arbitrary multimodal intervals can yield local candidates, not a guaranteed global minimum. Original closed interval endpoints are compared.\n\nLimitation: a