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Public evidence

math.linear_algebra

Machine-checked verification for calculation version 1.14.5 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.14.5 · engine_tested · 58/58 tests. It is not the current published claim. Current evidence is 1.14.16 (58/58 tests) · latest.

CVP status

CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Core assurance · all published modes

Order 2–4 square for solve/det/inverse/LU/Cholesky. qr, svd, and lstsq accept rectangular A with rows,cols ∈ [2,4]. Cholesky is SPD only (A = LLᵀ). Discovery pages lock one mode. Not a CAS, not Statistics regression, not large-matrix server compute. Scale fixtures cover named operations only; analytic eigen fixtures span 1e-250 through 1e250, and factor diagnostics use rounded published entries. Published subspace diagnostics use scaled QR/SVD projection; exact triangular spectra retain close diagonal values with sensitivity warnings. General 2×2 spectra additionally use 50 exact-input Fraction/Decimal references with an 8-ULP component bound; general 3–4 clustered/non-normal spectra and complex eigenbasis conditioning still require further review.

Declared partition coverage
PASS · 19/19 declared partitions (solve, det, inverse, multiply, transpose, rank, eigen, lu, chol, qr, svd, lstsq, rref, condition, nullspace, columnspace, rowspace, leftnullspace, invalid-domain)
Versions
Calculation 1.14.5 · CVP protocol 1.0.0-proposed · Evidence 2026-10-08.exact-2x2-clustered-spectrum
Verification revision
2026-10-08.exact-2x2-clustered-spectrum · 10/10 property · digest 6d520299f0f8

Verification

Legacy regression suite: 58/58 calculation tests · Production surface contract 5/5

Three distinct suites: educational examples on the calculator page, this legacy regression count (58/58 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 1.14.16 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-08.exact-2x2-clustered-spectrum. Calculation version 1.14.5. CVP 1.0.0-proposed. 179/179 golden · 8/8 CVP boundary · 14/14 invalid · 10/10 property · 1/1 metamorphic · 21/21 cross-interface · 2/2 cross-calculator · 5/5 CVP contract. digest 6d520299f0f8.

  • Golden (oracle-backed) 179 / 179
  • CVP boundary 8 / 8
  • Invalid input 14 / 14
  • Property 10 / 10
  • Metamorphic 1 / 1
  • Cross-interface 21 / 21
  • Cross-calculator 2 / 2
  • CVP contract 5 / 5
  • 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.
  • Verified scope all published modes
  • Assurance Core
  • release artifacts aligned PASS
  • schema output required declared PASS
  • schema valid input executes PASS
  • engine success output validates schema PASS
  • rest success payload validates schema PASS

Fingerprint sha256:3c45d6829aaad6cf56d4b8f52aeef8d8113a87a8a30395ed539cb129a05e7587

Input schema sha256:2064b1b78fdcd9902cf2c8376d8186372cd195517ef0c18d3b1a99ee8b3117c6 · Output schema sha256:53c249ee941a886f8103f7445e292a4246431e718cd0eacab96c0714ba1957cd · 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
2026-10-08
Evidence core
2026-10-08T13:23:06.328Z
Rendered
2026-10-08T13:26:13.063Z
Last reviewed
—

Assumptions

  • Real matrices
  • Order ≤ 4 square for solve/det/inverse/factorizations
  • lstsq also A ∈ R^{m×n} with m,n ∈ [2,4]
  • Planar ℝ² figure when 2×2; other shapes omit it
  • Not a CAS

Limitations

  • Order ≤ 4 (local small-matrix seed)
  • Singular inverse → SINGULAR_MATRIX
  • qr, svd, and lstsq accept rectangular m×n with m,n ∈ [2,4]; solve / det / inverse / LU / Cholesky stay square
  • Cholesky is SPD only (NOT_SYMMETRIC / NOT_POSITIVE_DEFINITE)
  • Not Statistics regression / large-matrix server compute
  • Not 2-norm κ₂ as a product / CAS / Jordan form

Sources

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

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.