Public evidence

math.polynomial.roots

Machine-checked verification for calculation version 1.2.0 · tier engine_tested

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Verification

21/21 calculation tests · Production surface contract 1/1

Golden tests 7 / 7
Boundary tests 6 / 6
Property tests 8 / 8
Production surface contract 1 / 1
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.2.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
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 sha256:40fcf2aa9a7d68d99caf6407235c97f4a3bf06a25d0b47bd7f9698f17195006c

Input schema sha256:65d482d3a36aa5453cecffa17353a93c971964d4c0b7180f151dc0a3a6e6e16e · Output schema sha256:3e0d7e31c5d09b7cccfa1770bfb7f726f6233642226cbec5d42011e03ca9f36c · 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: 2026-09-19T22:24:04.594Z
Rendered: 2026-09-20T09:07:29.787Z
Last reviewed: —

Assumptions

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

Limitations

Not /calc/math/quadratic (discriminant / vertex / parabola)
Not Ferrari quartic closed form
Not a single numerical root
Not symbolic CAS factoring
Not polynomial expansion
Degree ≤ 8
Leading coefficient must be nonzero
method=evaluate requires x

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=cardano · cubic_case=three_real · Actual n=3 · delta=-0.037037037037 · method=all_roots · solver=cardano · degree=3 · residual_max=0 · polynomial=x³ − 6x² + 11x − 6 · cubic_case=three_real
`golden-cardano-abcd`	golden	pass	Expected n=3 · degree=3 · solver=cardano · cubic_case=three_real · Actual n=3 · delta=-0.037037037037 · method=cardano · solver=cardano · degree=3 · residual_max=0 · polynomial=x³ − 6x² + 11x − 6 · cubic_case=three_real
`golden-cardano-one-real`	golden	pass	Expected n=3 · degree=3 · solver=cardano · cubic_case=one_real · Actual n=3 · delta=0.25 · method=cardano · solver=cardano · degree=3 · residual_max=1.31607134029e-12 · polynomial=x³ − 1 · cubic_case=one_real
`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
`golden-horner-17`	golden	pass	Expected value=17 · solver=horner · n_mul=2 · Actual value=17 · method=evaluate · solver=horner · degree=2 · x=2 · n_mul=2 · polynomial=3x² + 2x + 1 · formula=p(x) = ((cₙ x + cₙ₋₁) x + … ) x + c₀
`golden-horner-root`	golden	pass	Expected value=0 · solver=horner · Actual value=0 · method=evaluate · solver=horner · degree=3 · x=2 · n_mul=3 · polynomial=x³ − 6x² + 11x − 6 · formula=p(x) = ((cₙ x + cₙ₋₁) x + … ) x + c₀
`boundary-evaluate-missing-x`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-factor`	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
`property-poly-cardano`	property	pass	x³−1 Cardano
`property-poly-horner`	property	pass	1+2x+3x² at 2
`property-poly-horner-naive`	property	pass	Horner matches monomial sum