{ "protocol": { "name": "CVP", "version": "1.0.0-proposed", "revision": "2026-09-13", "spec_sha256": "f62725968356c92930531cd6085db76e216da06e95be53d636b0d2cf3218b148", "spec": "https://www.calculatorx.com/developers/cvp/spec/1.0" }, "document_status": "proposed", "calculator": { "id": "linear-system", "version": "1.14.1", "title": "Linear System / Small Matrix Calculator", "formula_family": "linear_algebra", "capability_id": "math.linear_algebra", "verification_revision": "2026-10-07.solve-publication-diagnostics" }, "profile": "core", "verified_scope": "all published modes", "status": "STALE", "verification_status": "VERIFIED", "production_freshness": "STALE", "overall_trust": "VERIFIED_STALE", "runner": { "name": "cvp-runner", "version": "1.0.0" }, "environment": { "runtime": "node", "runtime_version": "20.19.2", "numeric_model": "IEEE-754 binary64", "os": "darwin" }, "suite": { "id": "linear-system", "version": "1.14.1", "uri": "https://www.calculatorx.com/evidence/math.linear_algebra/1.14.1.json", "verification_revision": "2026-10-07.solve-publication-diagnostics" }, "obligation_set": [ "CVP-PROV-01", "CVP-MODEL-01", "CVP-SCOPE-01", "CVP-UNIT-01", "CVP-REF-01", "CVP-GOLD-01", "CVP-BND-01", "CVP-INV-01", "CVP-NUM-01", "CVP-COV-01", "CVP-CONTRACT-01", "CVP-DEP-01", "CVP-ART-01", "CVP-PROD-01", "CVP-DIM-01", "CVP-PROP-01", "CVP-META-01", "CVP-XCAL-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "ISO 80000-2:2019 Quantities and units — Mathematics", "kind": "standard", "reference": "Matrix, determinant, inverse, and rank notation for order 2–4" }, { "label": "CRC / Strang — Ax=b, LU/QR/SVD, four fundamental subspaces", "kind": "other", "reference": "LU + partial pivoting solve; det; Gauss–Jordan inverse; rank-nullity; Householder QR; one-sided Jacobi SVD; RREF; κ₁(A)" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "O2 Leibniz det, Cramer, cofactor inverse, minor-rank, Gram–Schmidt QR, column-wise Cholesky, closed-form 2×2/3×3 eigen vs IUT LU-solve / Householder / one-sided Jacobi SVD / Faddeev" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "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." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O2 expected_values + O2 numerical_behavior" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "29/29 legacy golden; 26/26 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "5/5 numeric-edge Evidence + 3/3 near-singularity numeric; illegal enum/system is Invalid only" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "6 Evidence illegal-input + 8/8 oracle-backed error-code (exact_error_match, not ULP)" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "max_error_observed_ulp=0; policy declared a priori" }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "19/19 declared partitions (solve, det, inverse, multiply, transpose, rank, eigen, lu, chol, qr, svd, lstsq, rref, condition, nullspace, columnspace, rowspace, leftnullspace, invalid-domain) · 29 legacy golden / 8 CVP boundary unique cases · 6 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "5/5 CVP contract · 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" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine linear-algebra; Node binary64" }, "CVP-ART-01": { "result": "PASS", "applicability": "required", "notes": "release_integrity.status=verified · digests: artifact_evidence_sha256=Evidence core (Trust freshness) · cvp_evidence_digest=artifacts.evidence_digest (fingerprint v2) · evidence_bundle_sha256=legacy Evidence JSON bytes · evidence_catalog_digest=attested_catalog_sha256 · production_sha256=bound production report · see artifacts.digest_registry" }, "CVP-PROD-01": { "result": "PASS", "applicability": "required", "notes": "Capability production binding: STALE · Site report: stale · STALE (freshness / digest drift after last PASS snapshot) · site report stale · local checks pass · local production checks PASS; capability production binding is not CURRENT — final status must stay STALE, not VERIFIED · attestation_id=b6db86a3946922a6529492107ca8043828115b3ffd21d9c4669ff69fb7f854ce · Capability production binding: STALE · Site report: STALE · Public schema 1.14.1 observed · production binding STALE · Semantic contract ✓ · Last attestation PASS · Evidence changed after the last successful production attestation. Re-attestation required. · Public/cache ✓ · Origin ✓ · schema_const=1.14.1 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-latest-alias-agrees=pass · cvp-immutable-manifest-fetch=pass · cvp-immutable-manifest-sha256=pass · cvp-latest-alias-matches-immutable=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=8a224dbdcd21223942d0e73df9a3c58e3b2c63d744bd5164790a86cc92da0fc9 · verified_at=2026-10-06T22:48:30.896Z · evidence_attested_at=2026-10-06T22:48:30.896Z · last_confirmed_current_at=2026-10-06T22:48:30.896Z · rendered_at=2026-10-06T22:48:30.896Z · binds=cvp_core_sha256 · Capability production binding: STALE · Site report: STALE · Evidence changed after the last successful production attestation. Re-attestation required.", "check_result": "PASS", "production_state": "STALE", "binding_current": false }, "CVP-DIM-01": { "result": "PASS", "applicability": "applicable", "notes": "small real matrices" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "10/10 property · enumerated fixed assertions (not generated; no seed)" }, "CVP-META-01": { "result": "PASS", "applicability": "applicable", "notes": "1/1 metamorphic" }, "CVP-ROUND-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "No inverse / round-trip vectors in pack — control not in obligation set" }, "CVP-XCAL-01": { "result": "PASS", "applicability": "applicable", "notes": "2/2 cross-calculator · xcal-det-triple PASS vs math.vector; xcal-eigen-poly PASS vs math.polynomial.roots" }, "CVP-IFACE-01": { "result": "PASS", "applicability": "applicable", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). 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." }, "CVP-ORACLE-01": { "result": "SKIP", "applicability": "higher_assurance", "notes": "O2 present; O3 not required this wave" }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "named expert review not performed" } }, "interfaces": { "compared": [ "ui-ssr", "rest", "mcp" ], "result": "PASS", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). 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." }, "artifacts": { "evidence_bundle_sha256": "10af22adc9d4a45b46ff55381dbe8c3070555fc1a5367cc9e5e1aadf7dc2c66d", "evidence_digest": "c6132667b855abd0feb0c8c825392fa0da5b61fb4972208aa0c0dbfc774bb951", "production_sha256": "8a224dbdcd21223942d0e73df9a3c58e3b2c63d744bd5164790a86cc92da0fc9", "attested_catalog_sha256": "6186d9f9c642e2b117ca4b72014d212f663656bb36624b7c12dbc67c29ee9f34", "production_checks": [ { "id": "math.linear_algebra:output-const", "status": "pass", "detail": "output const 1.14.0 vs capability 1.14.0", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" }, { "id": "math.linear_algebra:evidence-sha256", "status": "pass", "detail": "a29b01988ee8", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" }, { "id": "math.linear_algebra:semantic-contract", "status": "pass", "detail": "58/58", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" }, { "id": "math.linear_algebra:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.14.0 vs origin 1.14.0", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" }, { "id": "math.linear_algebra:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.linear_algebra/1.14.1/2026-10-07.solve-publication-diagnostics/core/c6132667b855", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z", "projection_compared": false }, { "id": "math.linear_algebra:cvp-latest-alias-agrees", "status": "pass", "detail": "math.linear_algebra/1.14.1/2026-10-07.solve-publication-diagnostics/core/c6132667b855", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z", "projection_compared": false }, { "id": "math.linear_algebra:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" }, { "id": "math.linear_algebra:cvp-immutable-manifest-sha256", "status": "pass", "detail": "7307c47e0dc1", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" }, { "id": "math.linear_algebra:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.linear_algebra/1.14.1/2026-10-07.solve-publication-diagnostics/core/c6132667b855", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z", "projection_compared": false }, { "id": "math.linear_algebra:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" }, { "id": "math.linear_algebra:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": false, "attestation_binding_current": false, "attested_at": "2026-10-06T22:48:30.896Z" } ], "digest_registry": { "digest_algorithm": "sha256", "canonicalization": "json-sorted-keys-utf8", "entries": [ { "name": "cvp_core_sha256", "field": "artifacts.cvp_core_sha256", "digest_scope": "cvp_verification_fingerprint_v2", "value": "c6132667b855abd0feb0c8c825392fa0da5b61fb4972208aa0c0dbfc774bb951", "note": "Immutable verification core; excludes attestation/live-status and Evidence contract counts" }, { "name": "cvp_evidence_digest", "field": "artifacts.evidence_digest", "digest_scope": "cvp_verification_fingerprint_v2", "value": "c6132667b855abd0feb0c8c825392fa0da5b61fb4972208aa0c0dbfc774bb951", "note": "Alias of cvp_core_sha256 (historical field name)" }, { "name": "artifact_evidence_sha256", "field": "release_integrity.digests.evidence_core_sha256", "digest_scope": "evidence_artifact_core", "value": "94e2f742f4c2a1f4c437fa367c6c80cf9f631c659baf8f41a2b29b1dede15930", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "6186d9f9c642e2b117ca4b72014d212f663656bb36624b7c12dbc67c29ee9f34", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "c6132667b855abd0feb0c8c825392fa0da5b61fb4972208aa0c0dbfc774bb951" }, "dependencies": [ { "name": "linear-algebra-engine", "version": "1.14.1" }, { "name": "linear-algebra-reference-oracle", "version": "1.0.0" }, { "name": "math.vector", "version": "1.6.1", "role": "cross_calculator_peer", "capability_id": "math.vector", "evidence_digest": "3e840b22dc12dce60edaa87d4f0b0749054aa01cbf39fc9ae4b70d1ab3c87bda", "evidence": "https://www.calculatorx.com/evidence/math.vector/1.6.1.cvp.json" }, { "name": "math.polynomial.roots", "version": "1.2.1", "role": "cross_calculator_peer", "capability_id": "math.polynomial.roots", "evidence_digest": "6a2ac2cde6219237c0e85a901d560fefaef70e930e49552531a6bb084084cd81", "evidence": "https://www.calculatorx.com/evidence/math.polynomial.roots/1.2.1.cvp.json" }, { "name": "node", "version": "20.19.2" } ], "attestation": { "status": "STALE", "href": "/.well-known/calculatorx-production-attestation.json", "id": "b6db86a3946922a6529492107ca8043828115b3ffd21d9c4669ff69fb7f854ce", "attested_at": "2026-10-06T22:48:30.896Z", "last_confirmed_current_at": "2026-10-06T22:48:30.896Z", "site_attestation_current": false, "capability_attestation_current": false, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-09-29T09:41:45.368Z", "live_updated_at": "2026-10-06T08:59:25.354Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-09-29T09:41:45.368Z", "site_stale_count": 4 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 4, "site_stale_capability_count": 4, "stale_reason": "Capability production binding: STALE · Site report: STALE · Evidence changed after the last successful production attestation. Re-attestation required.", "evidence_attested_at": "2026-10-06T22:48:30.896Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.14.1", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-06T22:48:30.896Z", "generated_at": "2026-10-06T22:48:30.896Z", "rendered_at": "2026-10-06T22:48:30.896Z", "notes": "verified_at/generated_at mark the first publication of this cvp_core_sha256 (artifacts.evidence_digest alias) for suite verification. evidence_attested_at/attested_at is the first production bind of that core digest. last_confirmed_current_at is the latest site-wide report that still confirms CURRENT. rendered_at is this JSON serialization and is not part of cvp_core_sha256 / evidence_digest. Production attestation binds cvp_core_sha256 (binds evidence_digest). Causal order: verified_at ≤ evidence_attested_at ≤ last_confirmed_current_at. attestation.bound_snapshot.site_stale_count is the site-wide stale capability count at Manifest bind time — not a live value. Fetch attestation.live_site_status.href for the current site report." }, "tests": { "golden": { "passed": 26, "total": 26, "failed": 0 }, "boundary": { "passed": 8, "total": 8, "failed": 0 }, "invalid": { "passed": 14, "total": 14, "failed": 0, "comparison": "exact_error_match" }, "property": { "passed": 10, "total": 10, "failed": 0, "kind": "fixed" }, "round_trip": { "passed": 0, "total": 0, "failed": 0 }, "metamorphic": { "passed": 1, "total": 1, "failed": 0 }, "contract": { "passed": 5, "total": 5, "failed": 0 }, "cross_interface": { "passed": 9, "total": 9, "failed": 0 }, "cross_calculator": { "passed": 2, "total": 2, "failed": 0 } }, "numerical": { "representation": "IEEE-754 binary64 small-matrix algebra; IUT publishes toPrecision(12) / roundSmart", "tolerance": { "type": "relative", "value": 1e-10, "rationale": "O2 uses Leibniz determinants, Cramer, cofactor inverse, minor-rank, Gram–Schmidt QR, column-wise Cholesky, and closed-form 2×2/3×3 eigen — not IUT Gaussian/Householder/Faddeev transcription. Relative 1e-10 covers presentation rounding; declared a priori.", "declared_before_evaluation": true }, "max_error_observed": 0 }, "coverage": { "partitions": [ { "id": "solve", "description": "solve", "exercised": true, "case_count": 32 }, { "id": "det", "description": "det", "exercised": true, "case_count": 4 }, { "id": "inverse", "description": "inverse", "exercised": true, "case_count": 2 }, { "id": "multiply", "description": "multiply", "exercised": true, "case_count": 1 }, { "id": "transpose", "description": "transpose", "exercised": true, "case_count": 1 }, { "id": "rank", "description": "rank", "exercised": true, "case_count": 3 }, { "id": "eigen", "description": "eigen", "exercised": true, "case_count": 4 }, { "id": "lu", "description": "lu", "exercised": true, "case_count": 2 }, { "id": "chol", "description": "chol", "exercised": true, "case_count": 5 }, { "id": "qr", "description": "qr", "exercised": true, "case_count": 6 }, { "id": "svd", "description": "svd", "exercised": true, "case_count": 7 }, { "id": "lstsq", "description": "lstsq", "exercised": true, "case_count": 8 }, { "id": "rref", "description": "rref", "exercised": true, "case_count": 3 }, { "id": "condition", "description": "condition", "exercised": true, "case_count": 3 }, { "id": "nullspace", "description": "nullspace", "exercised": true, "case_count": 4 }, { "id": "columnspace", "description": "columnspace", "exercised": true, "case_count": 3 }, { "id": "rowspace", "description": "rowspace", "exercised": true, "case_count": 3 }, { "id": "leftnullspace", "description": "leftnullspace", "exercised": true, "case_count": 3 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 14 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Ax=b, det, inverse, rank, LU/Cholesky/QR/SVD, eigen, RREF, condition, four fundamental subspaces" }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module linear-algebra oracle — Leibniz det, Cramer solve, cofactor inverse, minor rank, Gram–Schmidt QR, column-wise Cholesky, closed-form eigen (same runtime as IUT; not IUT transcription)", "engine": { "name": "linear-algebra-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O2 module backs unrounded identities vs IUT roundSmart — relative 1e-10 / 16 pub ULP", "engine": { "name": "linear-algebra-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.linear_algebra/1.14.1.json", "evidence_page": "https://www.calculatorx.com/evidence/math.linear_algebra/1.14.1", "calculator": "https://www.calculatorx.com/calc/math/linear-system", "schema": "https://www.calculatorx.com/developers/cvp/schema/cvp-evidence-1.0.json", "protocol": "https://www.calculatorx.com/developers/cvp/spec/1.0", "manifest": "https://www.calculatorx.com/evidence/math.linear_algebra/1.14.1.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.linear_algebra/1.14.1/2026-10-07.solve-publication-diagnostics.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.linear_algebra/1.14.1/2026-10-07.solve-publication-diagnostics.c6132667b855.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }