CVP verified calculation capability
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.
Math · Geometry Capability ID math.geometry.circle version 1.2.0 CVP VERIFIED CURRENT Core
Circumference
C = 2πrA = πr²s = r θCanonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit policy | Role |
|---|---|---|---|
r | length | consistent length unit | input / output |
radius | length | consistent length unit | input |
diameter | length | consistent length unit | input / output |
d | length | consistent length unit | input |
circumference | length | consistent length unit | input / output |
area | area | square of input unit | input / output |
theta_deg | scalar plane angle | — | input / output |
theta | scalar plane angle | — | input |
arc_length | length | consistent length unit | output |
sector_area | area | square of input unit | output |
theta_rad | scalar plane angle | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | closed circle / sector / arc identities (π r², 2πr, …) |
valid_domain | r > 0; finite signed degree angles and multiple turns. All nonzero outputs must be normal finite binary64 numbers (magnitude at least 2^-1022); exact zero angles are supported. NUMERIC_RANGE rejects underflow, overflow, or subnormal outputs; rescale length units or angles. |
singularity_policy | VALUE_MUST_BE_POSITIVE when r ≤ 0; NUMERIC_RANGE outside the normal finite output envelope |
branch_policy | not applicable — real principal value only |
tolerance | runtime_tolerance: 12 significant digits; nonzero values are never clamped by an absolute epsilon; verification_tolerance: relative 1e-10 against independent expected values; exact zeros and numeric types are checked separately |
convergence | not applicable — non-iterative |
conditioning | Relative input sensitivities: C and diameter to r = 1; disk area to r = 2; radius from area = 1/2. For nonzero arc/sector, relative error contributions are dr/r + dtheta/theta and 2dr/r + dtheta/theta respectively. Relative error is undefined at zero angle; use absolute error there. Conversion underflow and the normal-output envelope are separate limits. |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | Version-locked model with 12 significant-digit output rounding; tolerance-based cross-runtime agreement, not a historical engine or bitwise replay guarantee. |
independent_oracle | cvp:math.geometry.circle O2 / Evidence published cases |
golden_vectors | Evidence golden + boundary + property (and published_reference_case when listed) |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
r=1 → C=2π, A=π
CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.
Human page, REST, and MCP share the same engine and calculation_version.
Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json
and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 5/5.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/circle' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"from_radius","r":1},"calculation_version":"1.2.0"}'{
"inputs": {
"mode": "from_radius",
"r": 1
},
"calculation_version": "1.2.0"
}POST /api/v1/calc/circle. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Declared calculation modes for this capability.
from_radiusfrom_diameterfrom_circumferencefrom_areaarcsectorHuman-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior
Inspect, then execute. Same engine as REST and the human calculator.
curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: inspect_capability' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.geometry.circle"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: execute_calculation' \
-d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.geometry.circle","inputs":{"mode":"from_radius","r":1},"calculation_version":"1.2.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.2.0) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.