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Public evidence

math.linear_algebra

Machine-checked verification for calculation version 1.2.0 · tier engine_tested

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Verification

18/18 calculation tests · Production surface contract 3/3

  • Golden tests 7 / 7
  • Boundary tests 2 / 2
  • Property tests 9 / 9
  • Production surface contract 3 / 3
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  • Engine tested Yes
  • Source checked Yes
  • Artifact integrity PASS
  • Production attestation Embedded snapshot: STALE · Last attested schema matched 1.2.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · 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 PASS
  • Origin PASS
  • Supplemental domain review Not performed
  • Named expert review Not performed
  • release artifacts aligned PASS
  • schema valid input executes PASS
  • engine success output validates schema PASS

Fingerprint sha256:71870adce80328743f66874aac6fb45d3d26bc74c0dbbe24ed82bd5cc5e39cb2

Input schema sha256:b4a37bc896da86edeea5877d92d13c5d1970a5c4515462b3dbae29be0983e810 · Output schema sha256:f42f187a538de001c137f27aafbff93258631b63c9746b8a856bc452f8138785 · 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
linear-system
Engine
linear-algebra
Engine build
2026-09-19
Evidence core
2026-09-19T00:49:10.356Z
Rendered
2026-09-19T02:14:29.320Z
Last reviewed
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Assumptions

  • Real matrices
  • Order ≤ 4
  • Not a CAS

Limitations

  • Order ≤ 4 (local small-matrix seed)
  • Singular inverse → SINGULAR_MATRIX
  • Not SVD / large-matrix server compute

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-2x2goldenpassExpected x=2 · y=1 · status=unique · Actual mode=solve · order=2 · x=2 · y=1 · status=unique · det=1 · formula=Ax = b · algorithm=inverse_multiply
golden-detgoldenpassExpected det=-2 · Actual mode=det · order=2 · det=-2 · formula=det(A) · algorithm=gaussian_elimination · numeric_backend=float64 · singularity_threshold=1e-15 · condition_number=21
golden-rank-singulargoldenpassExpected rank=1 · det=0 · Actual mode=rank · order=2 · rank=1 · det=0 · formula=rank via Gaussian elimination · algorithm=gaussian_elimination · numeric_backend=float64 · singularity_threshold=1e-15
golden-identity-3goldenpassExpected x=4 · y=5 · z=6 · Actual mode=solve · order=3 · x=4 · y=5 · z=6 · status=unique · det=1 · formula=Ax = b
golden-eigen-diaggoldenpassExpected {"eigenvalues":[{"re":2,"im":0},{"re":3,"im":0}]} · Actual mode=eigen · order=2 · eigenvectors_found=2 · residual_max=0 · char_poly=x² − 5x + 6 · solver=quadratic · det=6 · formula=det(A − λI) = 0
golden-lugoldenpassExpected singular=false · Actual mode=lu · order=2 · singular=false · reconstruction_residual=0 · det=1 · formula=PA = LU · algorithm=lu_partial_pivoting · numeric_backend=float64
golden-qrgoldenpassExpected reconstruction_residual=0 · Actual mode=qr · order=2 · reconstruction_residual=0 · orthogonality_residual=0 · formula=A = QR (Householder) · algorithm=householder_qr · numeric_backend=float64 · singularity_threshold=1e-15
boundary-singularboundarypassExpected SINGULAR_MATRIX · Actual SINGULAR_MATRIX
boundary-svdboundarypassExpected INVALID_MODE · Actual INVALID_MODE
property-la-solvepropertypass2x+y=5
property-la-detpropertypassdet
property-la-invpropertypassdiag inverse
property-la-rankpropertypassrank-1 singular
property-la-tpropertypasstranspose
property-la-qrpropertypassQR residual
property-la-lupropertypassLU residual
property-la-eigenpropertypassdiag eigen
property-la-id3propertypassI₃ solve