Public evidence

mechanical.statics.hollow_circular_section

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

Physics L1 gap capability

Declared partition coverage: PASS · 2/2 declared partitions (domain, invalid-domain)
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-10-28.meta-metrics-v2
Verification revision: 2026-10-28.meta-metrics-v2 · 0/0 property · digest f82a75ad3cba

Verification

Legacy regression suite: 7/7 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (7/7 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 1.0.0 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 2026-10-28.meta-metrics-v2. Calculation version 1.0.0. CVP 1.0.0-proposed. 1/1 golden · 4/4 CVP boundary · 4/4 invalid · 2/2 metamorphic · 1/1 cross-interface · 6/6 CVP contract. digest f82a75ad3cba.

Golden (oracle-backed) 1 / 1
CVP boundary 4 / 4
Invalid input 4 / 4
Metamorphic 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:c2e00476fca982a75b25924b778f0c7d599305394eebf6fe8a76276ae45ce6ff

Input schema sha256:327427afcd54f2994cec9e971928a03cc20505ee1b6b5d497f30e283d0a85009 · Output schema sha256:4d214d01b4b34b6a42f8adafe08061f8445f65f8efe7c9b92ea9088d784a0503 · 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: hollow-circular-section
Engine: hollow-circular-section
Engine build: 2026-09-27
Evidence core: 2026-09-27T08:15:46.336Z
Rendered: 2026-11-10T05:18:42.175Z
Last reviewed: —

Limitations

Hollow circle about centroidal diameters
Ix = Iy = π(R⁴−r⁴)/4
Sx = Sy = Ix/R
kx = ky = √(R²+r²)/2
Not a solid circle, a rectangle, bending stress, or a plastic modulus

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

Hibbeler, Engineering Mechanics: Statics — Moments of inertia — circular area
Supports: The centroidal moment of a hollow circle about a diameter is π(R⁴−r⁴)/4.
Gere and Goodno, Mechanics of Materials — Moments of inertia — circular area
Supports: Supports the page formula: Ix = Iy = π(R⁴−r⁴)/4

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.