CVP verified calculation capability

Pythagorean theorem Calculation Capability

Right-triangle solve a² + b² = c² for a missing side, plus area and perimeter; verify mode when all three sides given.

Math Capability ID math.pythagorean version 1.2.0 CVP VERIFIED CURRENT Engineering

Model

Theorem

Theorem: a² + b² = c²
Hypotenuse: c = √(a² + b²)
Leg a: a = √(c² − b²)
Leg b: b = √(c² − a²)
Area: A = ab / 2
Perimeter: P = a + b + c

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit policy	Role
`a`	leg length	consistent length unit	input / output
`aInput`	leg length	consistent length unit	input
`leg_a`	leg length	consistent length unit	input
`legA`	leg length	consistent length unit	input
`b`	leg length	consistent length unit	input / output
`bInput`	leg length	consistent length unit	input
`leg_b`	leg length	consistent length unit	input
`legB`	leg length	consistent length unit	input
`c`	hypotenuse length	consistent length unit	input / output
`cInput`	hypotenuse length	consistent length unit	input
`hypotenuse`	hypotenuse length	consistent length unit	input
`hyp`	hypotenuse length	consistent length unit	input
`solveFor`	—	—	input
`value`	—	—	output
`area`	area	square of input unit	output
`perimeter`	length	same length unit	output
`area_status`	—	—	output
`perimeter_status`	—	—	output
`algorithm`	—	—	output
`numeric_domain`	—	—	output
`exactness`	—	—	output
`numeric_backend`	—	—	output

Trusted Math contract

Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.

Field	Declaration
`numeric_domain`	real
`exactness`	float64
`algorithm`	Scaled hypot; cancellation-resistant scaled inverse square difference; scaled squared verification residual with nondegenerate geometry.
`valid_domain`	Positive finite binary64 sides; strict512character decimal strings, matching aliases; solve a/b/c or verify. Derived range failures are explicit null/status.
`singularity_policy`	SIDE_NOT_POSITIVE,NUMERIC_UNDERFLOW,INVALID_NUMBER for invalid raw sides;HYPOTENUSE_TOO_SHORT for normalizedc<=known leg;RESULT_OVERFLOW for unrepresentable solved side.
`branch_policy`	not applicable — real principal value only
`tolerance`	note: Complete side/area/perimeter4ULP vs independent Decimal2000;scaled diagnostics absolute2e-15,threshold rounding can affect boundary classification.
`convergence`	not applicable — non-iterative
`conditioning`	Inverse leg solve is input-sensitive near c=known leg. Decimal input first rounds to binary64; display12digits,scheme not to scale. Verify tolerance1e-6 is not exact equality.
`rounding`	ieee754_round_ties_to_even
`overflow`	ieee754_nonfinite_or_coded_error
`reproducibility`	deterministic algorithm + Capability@Version
`independent_oracle`	CPython Decimal2000 on exact normalized binary64 inputs; complete-result reference
`golden_vectors`	Evidence golden + boundary + property (and published_reference_case when listed)

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Right triangle; positive side lengths.
When solving for a leg, the supplied hypotenuse must exceed the supplied known leg (solve_for=a → require c>b; solve_for=b → require c>a).
Exactly two fields are inputs when solving. Explicit solve_for selects the output. If all three are supplied without solve_for, they are verified rather than overwritten.
Interactive evaluation, shared URLs, and REST use the same engine, solve_for contract, and error codes.
Share URL is canonical: solve_for=a|b|c forces solve even if a leftover third side is present; mode=verify is required to stay in Verify after a tab change.

Example

One numerical check. The calculator page holds worked steps and FAQ.

a=3, b=4 → c=5

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance. 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.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (solve-c, solve-b, solve-a, verify, invalid-domain)
Calculation version: 1.2.0
Verification: 16/16 calculation tests · 6/6 legacy golden · 10/10 legacy boundary
Production surface contract: 6/6
Versions: Calculation 1.2.0 · CVP protocol 1.0.0-proposed · Evidence 2026-10-29.math-uuce-fields-v1
Verification revision: 2026-10-29.math-uuce-fields-v1 · 2/2 property · digest 8e57ac65e649
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Numerical scope: 93 independent full result packs across4operations and extreme scales; no exhaustive-domain claim
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 93/93 golden · 10/10 CVP boundary · 12/12 invalid · 2/2 property · 4/4 metamorphic · 4/4 cross-interface · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.2.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.2.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

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 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/pythagorean' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"a":3,"b":4,"solve_for":"c"},"calculation_version":"1.2.0"}'

{
  "inputs": {
    "a": 3,
    "b": 4,
    "solve_for": "c"
  },
  "calculation_version": "1.2.0"
}

POST /api/v1/calc/pythagorean. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: pythagorean
Engine: pythagorean
REST: POST /api/v1/calc/pythagorean
MCP: execute_calculation with capability_id: "math.pythagorean"
Agent input schema: Canonical (MCP / Agent)
REST input schema: Compatibility (tol[] / tol1…)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.2.0)
Versioned output schema: Immutable pin (1.2.0)

Operations

Declared calculation modes for this capability.

c
a
b
verify

References

Human-readable sources plus CVP reference evidence classes.

Sources

Euclid, Elements, Book I, Proposition 47 — In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle

Derived identities

Right-triangle area — A = ab/2

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

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.pythagorean"},"_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.pythagorean","inputs":{"a":3,"b":4,"solve_for":"c"},"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.