{
  "capability_id": "math.ratio",
  "tool_id": "ratio",
  "engine": "ratio",
  "calculation_version": "1.0.2",
  "generated_at": "2026-10-21T03:33:24.147Z",
  "engine_build": "2026-10-14",
  "test_count": 26,
  "passed": 26,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 11,
      "total": 11
    },
    "boundary": {
      "passed": 7,
      "total": 7
    },
    "property": {
      "passed": 8,
      "total": 8
    }
  },
  "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/ratio",
  "api": "https://www.calculatorx.com/api/v1/calc/ratio",
  "schema_input": "https://www.calculatorx.com/schemas/math.ratio.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.ratio.output.json",
  "assumptions": [
    "Finite rationals: integers, terminating decimals, or simple fractions a/b.",
    "Proportion denominators in A/B or C/D must be nonzero when used.",
    "Simplify / proportion / compare allow negative terms. Split does not."
  ],
  "limitations": [
    "Integers, terminating decimals, and simple a/b fractions only (no mixed numbers or scientific notation)",
    "Each term ≤ 48 decimal digits",
    "Simplify / proportion / compare allow negative terms",
    "Split requires every term ≥ 0 and Σ terms > 0 → SPLIT_NEGATIVE_TERM / SPLIT_ZERO_SUM",
    "All-zero simplify → ALL_ZERO",
    "Proportion needs exactly one blank among A,B,C,D → PROPORTION_ONE_BLANK",
    "Expert review pending — L1 engine-tested / source-checked"
  ],
  "boundary_conditions": [
    "Cannot simplify an all-zero ratio → ALL_ZERO",
    "Proportion needs exactly one blank among A,B,C,D → PROPORTION_ONE_BLANK",
    "Split requires every ratio term ≥ 0 → SPLIT_NEGATIVE_TERM",
    "Split requires Σ terms > 0 → SPLIT_ZERO_SUM",
    "Scale divide-by-zero → DIVISION_BY_ZERO"
  ],
  "sources": [
    {
      "title": "Encyclopedia of Mathematics — Greatest common divisor",
      "section": "Pairwise Euclidean GCF used after clearing denominators",
      "url": "https://encyclopediaofmath.org/wiki/Greatest_common_divisor",
      "supports": "Computation of the GCF of the integerized ratio terms after clearing denominators; multiple-term GCF is obtained iteratively (GCF(a,b,c)=GCF(GCF(a,b),c))",
      "kind": "reference"
    },
    {
      "title": "CalculatorX split convention",
      "section": "Nonnegative parts only",
      "supports": "Split requires every term ≥ 0 and Σ terms > 0, so shares are nonnegative allocations of a total",
      "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:dac908da70997d5d17219bced551bfbb3489d162043cbc082941e63da82008f4",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 26,
      "total": 26,
      "golden": 11,
      "boundary": 7,
      "property": 8
    },
    "contract_checks": {
      "passed": 10,
      "total": 10
    }
  },
  "evidence_core_generated_at": "2026-10-14T05:05:51.930Z",
  "rendered_at": "2026-10-21T03:33:24.147Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.2",
    "artifacts": {
      "engine": "1.0.2",
      "page": "1.0.2",
      "capability": "1.0.2",
      "evidence": "1.0.2",
      "input_schema": "1.0.2",
      "output_schema": "1.0.2",
      "mcp_contract": "1.0.2"
    },
    "digests": {
      "input_schema_sha256": "f265bc76ddf4ac054863a56d32fe03592f46d7a183cf98ad39c180496f456d46",
      "output_schema_sha256": "a88be281f59641c093c0fb7b28328ac502a4d55a7cda009c4ab75bc5f195a1ca",
      "evidence_sha256": "65b64ff7ff80866536f4899c310369a690d23d1224d90538271073019c78bc86",
      "evidence_core_sha256": "65b64ff7ff80866536f4899c310369a690d23d1224d90538271073019c78bc86",
      "capability_sha256": "f877414e3055735ae165e6dd82ceb8520e52aa54989b68be4bdd7e692ae08d4f",
      "engine_sha256": "6ef38e64f6a7018cce0538e78ba57c8e2a141f11e8779e9e3f91408a668b7b71",
      "mcp_contract_sha256": "0adfc6792fb2bdb38e7f8c92d2a3fddb0c94ca3cca44a7222de20471d2659c90"
    },
    "contract_checks": {
      "total": 10,
      "passed": 10,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.2"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "explanation-formula-n-term",
          "status": "pass",
          "detail": "r₁:⋯:rₙ → (r₁′÷g):⋯:(rₙ′÷g), rᵢ′=L·rᵢ, L=LCM(dᵢ), g=GCF(|rᵢ′|)"
        },
        {
          "id": "explanation-steps-match-result",
          "status": "pass"
        },
        {
          "id": "explanation-inputs-summary",
          "status": "pass"
        },
        {
          "id": "explanation-calculation-version",
          "status": "pass",
          "detail": "1.0.2"
        },
        {
          "id": "explanation-arity",
          "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"
  }
}
