{
  "capability_id": "engineering.uncertainty.coverage_factor",
  "tool_id": "coverage-factor",
  "engine": "coverage-factor",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:03:43.735Z",
  "engine_build": "2026-09-16",
  "test_count": 10,
  "passed": 10,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 1,
      "passed": 1
    },
    "boundary": {
      "total": 5,
      "passed": 5
    },
    "property": {
      "total": 4,
      "passed": 4
    }
  },
  "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/engineering/coverage-factor",
  "api": "https://www.calculatorx.com/api/v1/calc/coverage-factor",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.uncertainty.coverage_factor.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.uncertainty.coverage_factor.output.json",
  "assumptions": [
    "JCGM 100:2008 G.3 / G.4 two-sided coverage factor",
    "Default confidence p = 0.95",
    "Infinite ν uses the standard-normal quantile",
    "Not expanded U = k·u_c and not GUM model combination"
  ],
  "limitations": [
    "Does not compute expanded U = k·u_c (use Uncertainty propagate)",
    "Does not combine a measurement model",
    "Does not look up ν_eff (use Welch–Satterthwaite)"
  ],
  "boundary_conditions": [
    "missing nu → MISSING_REQUIRED_INPUT",
    "ν ≤ 0 and not inf → VALUE_MUST_BE_POSITIVE",
    "confidence not in (0, 1) → VALUE_OUT_OF_RANGE"
  ],
  "sources": [
    {
      "title": "JCGM 100:2008 (GUM) — Evaluation of measurement data",
      "section": "G.3 / G.4 Coverage factor and effective degrees of freedom",
      "url": "https://www.bipm.org/en/committees/jc/jcgm/publications",
      "supports": "k = t_{(1+p)/2}(ν) for two-sided coverage; infinite ν uses the normal quantile",
      "kind": "standard"
    },
    {
      "title": "JCGM 100:2008 (GUM) — Evaluation of measurement data",
      "section": "Table G.1 Values of k_p",
      "url": "https://www.bipm.org/utils/common/pdf/jcgm/JCGM_100_2008_E.pdf",
      "supports": "For p=0.95 and ν→∞, k_p = 1.960",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:52484b2831509e6e36865a8b34a6238ce26d258becea8369ba2a0d004ef9bebc",
  "tests": [
    {
      "id": "golden-k",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "nu": 8,
        "confidence": 0.95
      },
      "expect": {
        "k": 2.306004135204166,
        "k_source": "student_t",
        "infinite": false
      },
      "expectWarning": null,
      "actual": {
        "k": 2.306004135203951,
        "confidence": 0.95,
        "nu": 8,
        "infinite": false,
        "k_source": "student_t"
      },
      "tol": 0.000002
    },
    {
      "id": "boundary-k-inf",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "nu": "inf",
        "confidence": 0.95
      },
      "expect": {
        "k": 1.959963984540054,
        "k_source": "normal",
        "infinite": true,
        "nu": null
      },
      "expectWarning": null,
      "actual": {
        "k": 1.9599628032771197,
        "confidence": 0.95,
        "nu": null,
        "infinite": true,
        "k_source": "normal"
      },
      "tol": 0.000002
    },
    {
      "id": "boundary-k-default-p",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "nu": 8
      },
      "expect": {
        "confidence": 0.95,
        "k": 2.306004135204166
      },
      "expectWarning": null,
      "actual": {
        "k": 2.306004135203951,
        "confidence": 0.95,
        "nu": 8,
        "infinite": false,
        "k_source": "student_t"
      },
      "tol": 0.000002
    },
    {
      "id": "boundary-k-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "confidence": 0.95
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "nu is required"
    },
    {
      "id": "boundary-k-p",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "nu": 8,
        "confidence": 1
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "confidence must be in (0, 1)"
    },
    {
      "id": "boundary-k-nu",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "nu": 0,
        "confidence": 0.95
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "nu must be greater than zero"
    },
    {
      "id": "property-k-t8",
      "ok": true,
      "kind": "property",
      "detail": "t_0.975(8)",
      "expect": 2.306004135204166,
      "actual": 2.306004135203951
    },
    {
      "id": "property-k-source",
      "ok": true,
      "kind": "property",
      "detail": "student_t",
      "expect": "student_t",
      "actual": "student_t"
    },
    {
      "id": "property-k-normal",
      "ok": true,
      "kind": "property",
      "detail": "normal",
      "expect": "normal",
      "actual": "normal"
    },
    {
      "id": "property-k-default-p",
      "ok": true,
      "kind": "property",
      "detail": "default 0.95",
      "expect": 0.95,
      "actual": 0.95
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 10,
      "total": 10,
      "golden": 1,
      "boundary": 5,
      "property": 4
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-16T05:28:40.984Z",
  "rendered_at": "2026-09-16T22:03:43.735Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
      "engine": "1.0.0",
      "page": "1.0.0",
      "capability": "1.0.0",
      "evidence": "1.0.0",
      "input_schema": "1.0.0",
      "output_schema": "1.0.0",
      "mcp_contract": "1.0.0"
    },
    "digests": {
      "input_schema_sha256": "20893f1fb226455a702cbda171b92f0b4b3d1c226266deecc18af0c59cd6ec83",
      "output_schema_sha256": "daaf8adbcbffabcd2ab99d1546bea58f7b62ec619902a8a0141e9ea3698fd2a1",
      "evidence_sha256": "f5193cd375f65091331be894d0dff3814af182e07a2ce9710256c914b4dc622c",
      "evidence_core_sha256": "f5193cd375f65091331be894d0dff3814af182e07a2ce9710256c914b4dc622c",
      "capability_sha256": "63dde20a2e170fef34c6985d8efe2fdcb51cb8ac9b2d394aaff8432f83c77d06",
      "engine_sha256": "c8d4ccdbfeaf61d7b024d4e1babb0c2ba3b324c1b37bd0cb456a526d8d2b1bd1",
      "mcp_contract_sha256": "863098b311a7b17dc4b229a6302b90b3545b175f716e5d84772c7be8e9716b86"
    },
    "contract_checks": {
      "total": 4,
      "passed": 4,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}
