Public evidence

math.pythagorean

Machine-checked verification for calculation version 1.1.2 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

Positive sides; solve a|b|c or verify

Declared partition coverage: PASS · 5/5 declared partitions (solve-c, solve-b, solve-a, verify, invalid-domain)
Versions: Calculation 1.1.2 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 4/4 property · digest 4847c211167f

Verification

Legacy regression suite: 16/16 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (16/16 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.1.2 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-16.sources-no-wolfram. Calculation version 1.1.2. CVP 1.0.0-proposed. 6/6 golden · 10/10 CVP boundary · 11/11 invalid · 4/4 property · 2/2 metamorphic · 2/2 round-trip · 1/1 cross-interface · 6/6 CVP contract. digest 4847c211167f.

Golden (oracle-backed) 6 / 6
CVP boundary 10 / 10
Invalid input 11 / 11
Property 4 / 4
Metamorphic 2 / 2
Round-trip 2 / 2
Cross-interface 1 / 1
CVP contract 6 / 6
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Assurance Engineering

release artifacts aligned PASS
schema output required declared PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS
rest success payload validates schema PASS

Fingerprint sha256:a40496b0892cba4f91d0d18120c44036050d53fa19d0629815fa70749cda2bc1

Input schema sha256:649f1060999b4745d0b5561292750c09cfe7706499d5aac9a640b1ddd3f27fb5 · Output schema sha256:8090cd31f6b9ccef124db3d56324b2dc84c07f739dc923e4c9aa2049ced56b94 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: pythagorean
Engine: pythagorean
Engine build: 2026-09-21
Evidence core: 2026-09-21T15:54:02.547Z
Rendered: 2026-09-21T16:00:36.112Z
Last reviewed: —

Assumptions

Right triangle; positive side lengths.
c > a and c > b when solving for a leg.
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.

Limitations

Sides must be positive → SIDE_NOT_POSITIVE
Need two of a,b,c (or verify with three) → MISSING_REQUIRED_INPUT

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic 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
Supports: Classical statement of the Pythagorean theorem used as the geometric identity a² + b² = c².
Right-triangle area — A = ab/2
Supports: Area of a right triangle is half the product of the legs that form the right angle. Perimeter is the sum of the three sides.

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`3-4-5`	golden	pass	Expected c=5 · area=6 · Actual value=5 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=c · mode_label=Solve hypotenuse · formula=c=√(a²+b²) · heading=Hypotenuse c
`5-13`	golden	pass	Expected b=12 · Actual value=12 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=b · mode_label=Solve leg b · formula=b=√(c²−a²) · heading=Leg b
`12-13`	golden	pass	Expected a=5 · Actual value=5 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=a · mode_label=Solve leg a · formula=a=√(c²−b²) · heading=Leg a
`7-9`	golden	pass	Expected c=11.40175425099138 · Actual value=11.40175425099138 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=c · mode_label=Solve hypotenuse · formula=c=√(a²+b²) · heading=Hypotenuse c
`verify-3-4-5`	golden	pass	Expected mode=verify · valid=true · c=5 · area=6 · perimeter=12 · Actual value=5 · calculation_version=1.1.2 · status=success · mode=verify · mode_label=Verify right triangle · formula=a²+b²=c² · heading=Valid right triangle · a=3
`solve-for-c-ignores-extra`	golden	pass	Expected mode=solve · solve_for=c · c=5 · Actual value=5 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=c · mode_label=Solve hypotenuse · formula=c=√(a²+b²) · heading=Hypotenuse c
`side-not-positive`	boundary	pass	Expected SIDE_NOT_POSITIVE · Actual SIDE_NOT_POSITIVE
`missing-inputs`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-py-neg`	boundary	pass	Expected SIDE_NOT_POSITIVE · Actual SIDE_NOT_POSITIVE
`boundary-py-zero`	boundary	pass	Expected SIDE_NOT_POSITIVE · Actual SIDE_NOT_POSITIVE
`boundary-py-hyp-eq-leg`	boundary	pass	Expected HYPOTENUSE_TOO_SHORT · Actual HYPOTENUSE_TOO_SHORT
`boundary-py-invalid-solve`	boundary	pass	Expected INVALID_SOLVE_FOR · Actual INVALID_SOLVE_FOR
`boundary-py-overflow`	boundary	pass	Expected RESULT_OVERFLOW · Actual RESULT_OVERFLOW
`boundary-py-huge`	boundary	pass	Expected c=1.414213562373095e+200 · Actual value=1.414213562373095e+200 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=c · mode_label=Solve hypotenuse · formula=c=√(a²+b²) · heading=Hypotenuse c
`boundary-py-tiny`	boundary	pass	Expected c=1.414213562373095e-200 · Actual value=1.414213562373095e-200 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=c · mode_label=Solve hypotenuse · formula=c=√(a²+b²) · heading=Hypotenuse c
`boundary-py-cancel-leg`	boundary	pass	Expected a=0.0001414213561611208 · Actual value=0.0001414213561611208 · calculation_version=1.1.2 · status=success · mode=solve · solve_for=a · mode_label=Solve leg a · formula=a=√(c²−b²) · heading=Leg a