Public evidence

mechanical.statics.hollow_circular_shear

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

4/4 calculation tests · Production surface contract 6/6

Golden tests 2 / 2
Boundary tests 2 / 2
Property tests 0 / 0
Production surface contract 6 / 6
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain CURRENT) @ 2026-09-23T21:48:15.717Z
Semantic contract PASS
Evidence attested at 2026-09-23T02:27:54.588Z
Last production check 2026-09-23T02:27:54.588Z
Public / cache —
Origin —
Supplemental domain review Not performed
Named expert review Not performed

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 sha256:2774cd42addde39f2ce10209631684c632fffd1634259d1404eaaccc08a911c1

Input schema sha256:a3adf6f42bd6e10de9368d3f0d94f917cc39635113fa8240a925eef0ab746e72 · Output schema sha256:7a314ec58b38b5ef2a57ccfb69f7146103c050663c7d156b4e472a046031b839 · 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-shear
Engine: hollow-circular-shear
Engine build: 2026-09-23
Evidence core: 2026-09-23T21:38:17.699Z
Rendered: 2026-09-23T21:48:01.337Z
Last reviewed: —

Limitations

Neutral axis of one hollow circle
Q = (2/3)(R³−r³)
Width at the axis is 2(R−r)
Not beam deflection

Sources

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

Hibbeler, Mechanics of Materials — Shear stress in a circular tube
Supports: At the neutral axis of a hollow circle, the first moment is (2/3)(R³−r³) and the width is the two wall thicknesses along the diameter.

Published checks

Golden, boundary, and property cases included in this evidence build.

ID	Kind	Status	Detail
`golden-two`	golden	pass	Expected tau=2.3767138168389708 · Q=4.666666666666667 · I=11.780972450961723 · b=2 · area=9.42477796076938 · model=hollow_circular_shear · Actual model=hollow_circular_shear · V=12 · R=2 · r=1 · area=9.42477796076938 · I=11.780972450961723 · Q=4.666666666666666 · b=2
`golden-sign`	golden	pass	Expected tau=-2.3767138168389708 · Actual model=hollow_circular_shear · V=-12 · R=2 · r=1 · area=9.42477796076938 · I=11.780972450961723 · Q=4.666666666666666 · b=2
`boundary-equal`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT