Public evidence

mechanical.beam.deflection

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest Reproduce MCP Review policy

CVP status

O3 Layer-A tabulated partitions only.

Declared partition coverage: PASS · 5/5 declared partitions (ss-point-midspan, cantilever-tip, composition, signed, invalid-domain)
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-27.o2-o3.parent.iface.o3fix
Verification revision: 2026-09-27.o2-o3.parent.iface.o3fix · 5/5 property · digest ce207633c7da

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.

STALE · Build schema 1.0.0 ready · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-27.o2-o3.parent.iface.o3fix. Calculation version 1.0.0. CVP 1.0.0-proposed. 5/5 golden · 2/2 CVP boundary · 6/6 invalid · 5/5 property · 1/1 metamorphic · 24/24 O3 · 2/2 cross-interface · 2/2 cross-calculator · 6/6 CVP contract. digest ce207633c7da. O2: delta vs composed Layer-A separate-module identities (≤2 ULP). Multi-load is Σ δ_i. Not FEM, not indeterminate, not generic multi-load max. ≤2 ULP vs O3 applies only to tabulated Layer-A partitions projected from published leaf mpmath tables (simply_supported×point×midspan, cantilever×point×tip, simply_supported×uniform×midspan). Multi-load composition is out of O3 claim scope.

Golden (oracle-backed) 5 / 5
CVP boundary 2 / 2
Invalid input 6 / 6
Property 5 / 5
Metamorphic 1 / 1
O3 high-precision 24 / 24
Cross-interface 2 / 2
Cross-calculator 2 / 2
CVP contract 6 / 6
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only. SSR Entry uses leaf-shaped query (prefill remap). REST/MCP use mechanical.beam.deflection contract inputs.
Verified scope Shared Euler–Bernoulli contract: support × loads[] × query; Layer-A closed forms via delegates; multi-load δ=Σδ_i; partitioned O3 for three Layer-A tip/midspan tables.
Assurance Engineering
Deferred Not FEM, not indeterminate, not Timoshenko, not generic multi-load max, not overhang, not cantilever triangular in v1.

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:b36e3be38b503f7db9952acc8a1993dcb17c5c9f64262ffc21ae22ab485cf26a

Input schema sha256:08167e0e426ef2ec8bea96b96c42fb0e21623e0c317a83d152146408edca0f5c · Output schema sha256:b806bb6cb02fdefe91ec172364023e8bfc4108b1157b2b799c1556fbf3bed630 · 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: mechanical-beam-deflection
Engine: mechanical-beam-deflection
Engine build: 2026-09-27
Evidence core: 2026-09-27T04:31:53.944Z
Rendered: 2026-09-27T07:46:57.267Z
Last reviewed: —

Limitations

Not FEM / indeterminate / Timoshenko
Not generic multi-load max
Not overhang; cantilever triangular deferred in v1
Human SEO Entries remain leaf discovery URLs until L1 hard-close

Sources

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

Hibbeler, Mechanics of Materials — Deflection of beams — simply supported beam with a concentrated load at midspan
Supports: The midspan deflection is P L³ / (48 E I) when the load sits at the center of a simply supported span.
Gere and Goodno, Mechanics of Materials — Deflection of beams — simply supported beam with a concentrated load at midspan
Supports: Supports the page formula: δ = P L³ / (48 E I)

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
`golden-ss-point-mid`	golden	pass	Expected delta=80 · model=mechanical.beam.deflection · Actual delta=80 · model=mechanical.beam.deflection · support=simply_supported · L=2 · E=1 · I=1 · x=1 · solver=beam.deflection superposition of Layer-A At-curves
`golden-cantilever-tip`	golden	pass	Expected delta=8 · model=mechanical.beam.deflection · Actual delta=8 · model=mechanical.beam.deflection · support=cantilever · L=2 · E=1 · I=1 · x=2 · solver=beam.deflection superposition of Layer-A At-curves
`golden-ss-uniform-mid`	golden	pass	Expected delta=80 · model=mechanical.beam.deflection · Actual delta=80 · model=mechanical.beam.deflection · support=simply_supported · L=2 · E=1 · I=1 · x=1 · solver=beam.deflection superposition of Layer-A At-curves
`golden-superpose-at`	golden	pass	Expected delta=18 · model=mechanical.beam.deflection · Actual delta=18 · model=mechanical.beam.deflection · support=simply_supported · L=2 · E=1 · I=1 · x=1 · solver=beam.deflection superposition of Layer-A At-curves
`boundary-empty-loads`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-E`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`property-check-80`	property	pass	ss×point×midspan δ=80