CVP verified calculation capability
Axis-aligned ellipse, parabola, and hyperbola. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page, not coordinate geometry, not CAS.
Math · Geometry Capability ID math.geometry.conic version 1.1.0 CVP VERIFIED CURRENT Core
Ellipse
x²/a² + y²/b² = 1x² = 4pyx²/a² − y²/b² = 1Modes: ellipse · oval · parabola · parabolic · hyperbola · hyperbolic
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit policy | Role |
|---|---|---|---|
a | length | consistent length unit | input / output |
b | length | consistent length unit | input / output |
p | length | consistent length unit | input / output |
orientation | — | — | input / output |
c | length | consistent length unit | output |
e | scalar ratio | — | output |
area | area | square of input unit | output |
perimeter | length | same length unit | output |
focus_x | length | consistent length unit | output |
focus_y | length | consistent length unit | output |
directrix | — | — | output |
asymptote_slope | scalar ratio | — | output |
equation | — | — | output |
circle | — | — | output |
major | length | consistent length unit | output |
minor | length | consistent length unit | output |
four_p | length | consistent length unit | output |
directrix_value | length | consistent length unit | output |
directrix_axis | — | — | output |
perimeter_method | — | — | output |
foci | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | scaled axis-aligned conic identities; factored normalized ellipse eccentricity; scaled Ramanujan I perimeter; hypot hyperbola focus |
valid_domain | strict decimal number/string input; positive a,b or nonzero signed p; nonzero inputs and reported numeric outputs must be finite normal binary64 (abs >= 2^-1022); exact zero for circular eccentricity/focus coordinates only |
singularity_policy | VALUE_MUST_BE_POSITIVE for nonpositive semiaxes; INVALID_INPUT for p=0; NUMERIC_UNDERFLOW for textual nonzero converted to zero; NUMERIC_RANGE on nonzero subnormal or overflowing output; rescale units |
branch_policy | not applicable — real principal value only |
tolerance | type: relative; value: 2e-12; note: Against independent high-precision values of the published formula, relative to normalized binary64 inputs; exact zero/discrete fields separately checked. No universal perimeter model-error bound is claimed. |
convergence | not applicable — non-iterative |
conditioning | Ellipse c and e near a=b are input-sensitive. Binary64 rounding can make distinct decimal axes equal; circle classification is exact equality after normalization. Eccentricity may round to 1 for very thin ellipses or near-degenerate hyperbolas. Perimeter is Ramanujan I approximation; numeric tolerance measures that formula, not error against exact arclength. |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | deterministic algorithm + Capability@Version |
independent_oracle | cvp:math.geometry.conic O2 Python mpmath high precision / private reference fixtures |
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.
ellipse a=5 b=4 → c=3, e=0.6
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/conic-section' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"ellipse","a":5,"b":4},"calculation_version":"1.1.0"}'{
"inputs": {
"mode": "ellipse",
"a": 5,
"b": 4
},
"calculation_version": "1.1.0"
}POST /api/v1/calc/conic-section. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Human-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.conic"},"_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.conic","inputs":{"mode":"ellipse","a":5,"b":4},"calculation_version":"1.1.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.1.0) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.