{
  "capability_id": "math.multiplication",
  "tool_id": "multiplication",
  "engine": "multiplication",
  "calculation_version": "1.0.4",
  "generated_at": "2026-10-22T08:54:35.136Z",
  "engine_build": "2026-10-22",
  "test_count": 15,
  "passed": 15,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 10,
      "total": 10
    },
    "boundary": {
      "passed": 5,
      "total": 5
    },
    "property": {
      "passed": 0,
      "total": 0
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/math/multiplication",
  "api": "https://www.calculatorx.com/api/v1/calc/multiplication",
  "schema_input": "https://www.calculatorx.com/schemas/math.multiplication.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.multiplication.output.json",
  "assumptions": [
    "Real decimal inputs parsed as exact decimal strings (integer mantissa × 10^−scale), not binary floating-point.",
    "Product mode and Long multiplication mode use the same exact mantissa multiplication; Long adds partial-product steps."
  ],
  "limitations": [
    "Exactness applies to accepted plain decimal tokens, not values rounded by a client before sending. Unsafe JSON integer numbers rejected; strings preserve full source digits.",
    "512 characters and48 significant digits per factor; trailing zeros count.",
    "Long grid limited to24 significant digits and24 displayed digit places per normalized factor; otherwise no work, LONG_GRID_TRUNCATED, and full exact product.",
    "productStr is authoritative; product is approximate or null on binary64 range loss. Share links use current engine, not historical replay."
  ],
  "boundary_conditions": [
    "Non-numeric input → error",
    "Scientific notation (e.g. 1.2e3) → error; use plain decimals only",
    "Product mode: up to 48 significant digits per factor",
    "Long visual grid: up to 24 significant digits and 24 normalized displayed digit places per factor; larger factors still return an exact product with LONG_GRID_TRUNCATED (working steps omitted — never silently truncated)"
  ],
  "sources": [
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Exact decimal place-count multiplication",
      "supports": "Long-multiplication algorithm with partial products; exact decimal mantissa × BigInt; sign rules for negatives.",
      "kind": "definition"
    },
    {
      "title": "Margaret Stevens — The Maths Workbook (University of Oxford)",
      "section": "Chapter 1, §1: Algebraic Expressions and Fractions; §3: Equations",
      "url": "https://www.some.ox.ac.uk/wp-content/uploads/2024/08/Maths-Workbook.pdf",
      "supports": "Algebraic addition/subtraction, multiplication/division, distributive rules, equivalent fractions, common denominators and reciprocals. Ratios are interpreted as quotients. Equality of ratios with nonzero denominators permits cross multiplication, and solving a proportion uses the chapter’s equation transformations. A zero divisor is excluded; integer quotient/remainder uses the separately cited Euclidean-division reference. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.",
      "kind": "reference",
      "publisher": "University of Oxford, Department of Economics; hosted by Somerville College"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:dc84c04067e841046fd9c44e75efea5679269b807bfae5230b0c8e203cf8e20b",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 15,
      "total": 15,
      "golden": 10,
      "boundary": 5,
      "property": 0
    },
    "contract_checks": {
      "passed": 5,
      "total": 5
    }
  },
  "evidence_core_generated_at": "2026-10-22T04:49:15.857Z",
  "rendered_at": "2026-10-22T08:54:35.136Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.4",
    "artifacts": {
      "engine": "1.0.4",
      "page": "1.0.4",
      "capability": "1.0.4",
      "evidence": "1.0.4",
      "input_schema": "1.0.4",
      "output_schema": "1.0.4",
      "mcp_contract": "1.0.4"
    },
    "digests": {
      "input_schema_sha256": "e8bea4b5fe595fab4051b788b43b902441dd63d870e9c76cec05ab4033bd806c",
      "output_schema_sha256": "571f599faa0525a92c76e3cc644e97f876caab84a844c897c0dd74dc9de904ce",
      "evidence_sha256": "dec6308790c26b8d47dcaa993b7c6d6e056f98ddfa7c9eebcd721ef6a19f9aab",
      "evidence_core_sha256": "dec6308790c26b8d47dcaa993b7c6d6e056f98ddfa7c9eebcd721ef6a19f9aab",
      "capability_sha256": "7be5e7aa7ac4ad019b04efec87a96d20f3f2a441108198a1b4e0aa182e3aa5cd",
      "engine_sha256": "a664ae25cd2134de7de43a99352933043215473589aec38c9416508150cb1008",
      "mcp_contract_sha256": "a1a8617719bef45391ee6917dc1783a01de2eedf297e7596b3cb5017cd0e1560"
    },
    "contract_checks": {
      "total": 5,
      "passed": 5,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.4"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  },
  "tests": [],
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}