Home Developers Evidence math.numerical.root

Public evidence

math.numerical.root

Machine-checked verification for calculation version 1.1.0 · tier engine_tested

Open calculator API Capability Download JSON MCP Review policy

Verification

13/13 calculation tests · Production surface contract 1/1

  • Golden tests 3 / 3
  • Boundary tests 3 / 3
  • Property tests 7 / 7
  • Production surface contract 1 / 1
    • }
  • Engine tested Yes
  • Source checked Yes
  • Artifact integrity PASS
  • Production attestation Embedded snapshot: STALE · Last attested schema matched 1.1.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · 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 PASS
  • Origin PASS
  • Supplemental domain review Not performed
  • Named expert review Not performed
  • release artifacts aligned PASS

Fingerprint sha256:52164a829d1fac966a8dcb56c30ffc306359d9a9f5c8eca9e36dd425b7758117

Input schema sha256:78e2b3d51ab5cf75f7930420a3332b2f153830641d99fad4cd2ff5f1aa61edd8 · Output schema sha256:891fdabb90a813b90738abd72a8cbffcbf432d753cb0301625c94ccbd74fd2fe · 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
numerical-root
Engine
numerical-root
Engine build
2026-09-19
Evidence core
2026-09-19T22:07:54.547Z
Rendered
2026-09-20T09:07:29.785Z
Last reviewed
—

Assumptions

  • Not CAS / not complex roots listed
  • Not a system of equations
  • Not all-roots of a polynomial
  • Not ⁿ√a
  • Polynomial degree ≤ 8

Limitations

  • Not ⁿ√a — that remains /calc/math/root
  • Not three independent Newton/bisection/secant product pages
  • Not CAS / not a nonlinear system
  • Degree > 8 → INVALID_INPUT
  • No convergence → NO_CONVERGENCE

Sources

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

Published checks

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

IDKindStatusDetail
golden-newton-sqrt2goldenpassExpected root=1.4142135623730951 · Actual method=newton · integrand=poly · root=1.41421356237 · residual=4.51061410445e-12 · iterations=4 · tol=1e-10 · formula=x ← x − f(x)/f′(x) · degree=2
golden-bisection-sqrt2goldenpassExpected root=1.4142135623730951 · Actual method=bisection · integrand=poly · root=1.41421356238 · residual=3.15445447541e-11 · iterations=30 · tol=1e-10 · formula=midpoint until sign change bracket shrinks · degree=2
golden-newton-singoldenpassExpected root=3.141592653589793 · integrand=sin · Actual method=newton · integrand=sin · root=3.14159265359 · residual=0 · iterations=4 · tol=1e-10 · formula=x ← x − f(x)/f′(x)
boundary-no-sign-changeboundarypassExpected INVALID_INPUT · Actual INVALID_INPUT
boundary-halleyboundarypassExpected INVALID_MODE · Actual INVALID_MODE
boundary-casboundarypassExpected INVALID_MODE · Actual INVALID_MODE
property-root-newtonpropertypass√2 newton
property-root-bisectpropertypass√2 bisection
property-root-secantpropertypass√2 secant
property-root-linpropertypassx-4=0
property-root-zeropropertypassx=0
property-root-sinpropertypasssin 3 → π
property-root-sin-bisectpropertypasssin bracket → π