{
  "capability_id": "math.gcf",
  "tool_id": "gcf",
  "engine": "gcf",
  "calculation_version": "1.0.2",
  "generated_at": "2026-10-20T13:36:50.744Z",
  "engine_build": "2026-10-14",
  "test_count": 20,
  "passed": 20,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 6,
      "total": 6
    },
    "boundary": {
      "passed": 7,
      "total": 7
    },
    "property": {
      "passed": 7,
      "total": 7
    }
  },
  "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/gcf",
  "api": "https://www.calculatorx.com/api/v1/calc/gcf",
  "schema_input": "https://www.calculatorx.com/schemas/math.gcf.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.gcf.output.json",
  "assumptions": [
    "Integer inputs; negatives treated by absolute value.",
    "Zeros are ignored unless every input is 0.",
    "GCF of a set of all zeros is undefined."
  ],
  "limitations": [
    "Integers only; negatives treated by absolute value",
    "Each integer ≤ 48 decimal digits (product bound, not a mathematical bound)",
    "Zeros are ignored unless every input is 0 (then UNDEFINED)",
    "Need at least two numbers → NEED_TWO_NUMBERS",
    "Non-integers → INVALID_NUMBER",
    "Integers beyond MAX_SAFE_INTEGER must be decimal strings in JSON"
  ],
  "boundary_conditions": [
    "Need at least two numbers → NEED_TWO_NUMBERS",
    "Missing list → MISSING_REQUIRED_INPUT",
    "Non-integers rejected → INVALID_NUMBER",
    "More than 48 digits → VALUE_ABOVE_MAX",
    "All zeros → UNDEFINED"
  ],
  "sources": [
    {
      "title": "Encyclopedia of Mathematics — Greatest common divisor",
      "section": "Definition; pairwise fold; prime-factor form",
      "url": "https://encyclopediaofmath.org/wiki/Greatest_common_divisor",
      "supports": "GCF of n integers exists when not all are zero; (a₁,…,aₙ,aₙ₊₁)=((a₁,…,aₙ),aₙ₊₁); shared-prime min exponents",
      "kind": "reference"
    },
    {
      "title": "Encyclopedia of Mathematics — Euclidean algorithm",
      "section": "Remainder recurrence GCF(a,b)=GCF(b, a mod b)",
      "url": "https://encyclopediaofmath.org/wiki/Euclidean_algorithm",
      "supports": "Binary Euclidean primitive used inside the pairwise fold",
      "kind": "reference"
    },
    {
      "title": "CalculatorX integer convention",
      "section": "Absolute value; zero-set; 48-digit BigInt domain",
      "supports": "Negatives by |n|; ignore zeros unless the whole set is 0; exact BigInt with a product digit cap",
      "kind": "definition"
    },
    {
      "title": "MIT Mathematics for Computer Science — Chapter 8: Number Theory",
      "section": "Chapter 8, including sections 8.2–8.9 and problem 8.24",
      "url": "https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-spring-2015/mit6_042js15_textbook.pdf",
      "supports": "Divisibility, prime factorization, gcd and the Euclidean algorithm, lcm via prime exponents, division with remainder, modular congruence and multiplicative inverses. CalculatorX’s signed-remainder and zero-input policies are stated separately on the page. Mathematical reference only; not validation or endorsement of this implementation.",
      "kind": "reference",
      "publisher": "Massachusetts Institute of Technology"
    }
  ],
  "methods": [
    "Pairwise Euclidean fold (canonical engine)",
    "Prime-factor GCF (cross-check when every |n| ≤ 1,000,000)",
    "Factor-list GCF (cross-check when every |n| ≤ 10,000)"
  ],
  "fingerprint": "sha256:ce4c8fd3816846a3947cf60cc5a029f9ac4466c2dbe18ebc7381d0b2803029fc",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 20,
      "total": 20,
      "golden": 6,
      "boundary": 7,
      "property": 7
    },
    "contract_checks": {
      "passed": 5,
      "total": 5
    }
  },
  "evidence_core_generated_at": "2026-10-14T04:17:16.233Z",
  "rendered_at": "2026-10-20T13:36:50.744Z",
  "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": "937a6e502dea5e3c5dfc1ddc415dfe74551baf9c69172984c2beceac52db1c58",
      "output_schema_sha256": "0197666ba550d0fd10d924e139641734a798a04db1fcf2a2b5f25113ce68d993",
      "evidence_sha256": "b67af2483f41e6041c73b9c44cc25978497fff687230ac7d9bf4c090452c3077",
      "evidence_core_sha256": "b67af2483f41e6041c73b9c44cc25978497fff687230ac7d9bf4c090452c3077",
      "capability_sha256": "1234f25b85f5ed592374e696724501b0b36cdf5e27fdc2f6fb889d80b439dde5",
      "engine_sha256": "6ef38e64f6a7018cce0538e78ba57c8e2a141f11e8779e9e3f91408a668b7b71",
      "mcp_contract_sha256": "ca1fff0bed6fbe68f06e2458301f283e6027f117efd28200e2aa0a1389387b19"
    },
    "contract_checks": {
      "total": 5,
      "passed": 5,
      "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": "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"
  }
}