Public evidence

math.polynomial.roots

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

12/12 calculation tests · Production surface contract 1/1

Golden tests 3 / 3
Boundary tests 4 / 4
Property tests 5 / 5
Production surface contract 1 / 1
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Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-19T00:00:17.039Z
Semantic contract PASS
Evidence attested at 2026-09-18T21:41:55.460Z
Last production check 2026-09-18T21:41:55.460Z
Public / cache —
Origin —
Supplemental domain review Not performed
Named expert review Not performed

release artifacts aligned PASS

Fingerprint sha256:f3f73837d774b8104ce7fcff47e182f781eb6d7b10ab90571a9f4f1e8e88fa16

Input schema sha256:90582b687e530878b80afd2e7f7677618ab4375357cb4cdfa3578afcadf10f34 · Output schema sha256:a2f6dbed117c9b3bc364cfa6673ad263420d04dd6c04e821555201d57630f281 · 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: polynomial-roots
Engine: polynomial-roots
Engine build: 2026-09-19
Evidence core: 2026-09-19T00:15:56.290Z
Rendered: 2026-09-19T02:14:29.322Z
Last reviewed: —

Assumptions

Real coefficients
Leading coefficient nonzero
Degree ≤ 8
Not a second quadratic page
Not CAS factoring

Limitations

Not /calc/math/quadratic (discriminant / vertex / parabola)
Not a single numerical root
Not symbolic CAS factoring
Degree ≤ 8
Leading coefficient must be nonzero

Sources

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

ISO 80000-2:2019 Quantities and units — Mathematics

Published checks

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

ID	Kind	Status	Detail
`golden-linear`	golden	pass	Expected n=1 · degree=1 · solver=linear · Actual n=1 · method=all_roots · solver=linear · degree=1 · residual_max=0 · polynomial=2x − 2 · formula=x = −c0/c1
`golden-quadratic`	golden	pass	Expected n=2 · degree=2 · solver=quadratic · Actual n=2 · method=all_roots · solver=quadratic · degree=2 · residual_max=0 · polynomial=x² − 6x + 8 · formula=x = (−b ± √(b² − 4ac)) / (2a)
`golden-cubic-123`	golden	pass	Expected n=3 · degree=3 · solver=durand_kerner · Actual n=3 · method=all_roots · solver=durand_kerner · degree=3 · residual_max=0 · polynomial=x³ − 6x² + 11x − 6 · formula=Durand–Kerner simultaneous iteration
`boundary-leading-zero`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-degree-zero`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-quadratic-method`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-cas`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`property-poly-linear`	property	pass	2x−2=0 → 1
`property-poly-quadratic`	property	pass	x²−6x+8
`property-poly-cubic`	property	pass	(x−1)(x−2)(x−3)
`property-poly-i`	property	pass	x²+1 → ±i
`property-poly-vieta`	property	pass	Vieta sum