{
  "capability_id": "engineering.uncertainty.coverage_factor",
  "calculation_version": "1.0.0",
  "protocol_version": "1.0.0-proposed",
  "protocol_document_status": "proposed",
  "verification_revision": "2026-09-16.o2-o3",
  "oracle": {
    "class": "O3",
    "library": "mpmath 1.4.1",
    "mpmath_dps": 80,
    "backend": null,
    "rounding": null,
    "generator_id": "coverage-factor-mpmath-o3",
    "generator_version": "1.0.0",
    "generator_sha256": "8151e922033511c290103334c5f27d5e463262d080e7c36604bd1deb8ea21ce3",
    "table_sha256": "9213aef2eb7e0658f5fa58a359ec01d581848a34001b0b63117a2d53ddcaa058",
    "seed": "20260916.coverage-factor-o3",
    "independent_of_iut": true
  },
  "claim_scope": "O2: two-sided k = t_{(1+p)/2}(ν) vs separate-module inverse (|Δk|≤2e-6). Infinite ν uses Φ⁻¹. Not U=k·u_c, not one-sided k. ≤2e-6 vs O3 applies only to the published tabulated k vectors (ν=8/1/2/30, inf, default p, p=0.99, nu_eff alias). It is not a whole-domain guarantee and does not cover U=k·u_c or one-sided k. Infinite-ν comparison is limited by the IUT Hastings erf polyfill when Math.erfc is absent.",
  "commands": {
    "regenerate_table": "python3 generate-coverage-factor-o3.py",
    "regenerate_table_repo": "python3 scripts/lib/cvp/oracles/generate-coverage-factor-o3.py",
    "independent_rest": "Compare POST /api/v1/calc/coverage-factor against /developers/cvp/reproduce/coverage-factor-o3-tables.json",
    "run_cvp": "npm run cvp:run -- --capability engineering.uncertainty.coverage_factor",
    "rest_example": "POST https://www.calculatorx.com/api/v1/calc/coverage-factor"
  },
  "public_files": {
    "table": "/developers/cvp/reproduce/coverage-factor-o3-tables.json",
    "table_url": "https://www.calculatorx.com/developers/cvp/reproduce/coverage-factor-o3-tables.json",
    "generator": "/developers/cvp/reproduce/generate-coverage-factor-o3.py",
    "generator_url": "https://www.calculatorx.com/developers/cvp/reproduce/generate-coverage-factor-o3.py",
    "checker": "/developers/cvp/reproduce/check-math-o3-rest.py",
    "checker_url": "https://www.calculatorx.com/developers/cvp/reproduce/check-math-o3-rest.py",
    "manifest": "/evidence/engineering.uncertainty.coverage_factor/1.0.0.cvp.json",
    "this_file": "/evidence/engineering.uncertainty.coverage_factor/reproduce.json"
  },
  "result_summary": {
    "passed": 8,
    "total": 8,
    "failed": 0,
    "max_error_ulp": 5319935312,
    "threshold_ulp": 0.000002,
    "max_threshold_ulp": 0.000002
  },
  "vectors": [
    {
      "id": "o3-t8",
      "kind": "student-t",
      "inputs": {
        "nu": 8,
        "confidence": 0.95
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "infinite": false,
        "k_source": "student_t",
        "nu": 8,
        "k": 2.3060041352041667,
        "confidence": 0.95
      },
      "actual": {
        "k": 2.306004135203951,
        "confidence": 0.95,
        "nu": 8,
        "infinite": false,
        "k_source": "student_t"
      },
      "error_ulp": 486,
      "threshold_ulp": 0.000002,
      "ok": true
    },
    {
      "id": "o3-inf",
      "kind": "infinite",
      "inputs": {
        "nu": "inf",
        "confidence": 0.95
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "infinite": true,
        "k_source": "normal",
        "nu": null,
        "k": 1.9599639845400543,
        "confidence": 0.95
      },
      "actual": {
        "k": 1.9599628032771197,
        "confidence": 0.95,
        "nu": null,
        "infinite": true,
        "k_source": "normal"
      },
      "error_ulp": 5319935312,
      "threshold_ulp": 0.000002,
      "ok": true
    },
    {
      "id": "o3-default",
      "kind": "default-p",
      "inputs": {
        "nu": 8
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "infinite": false,
        "k_source": "student_t",
        "nu": 8,
        "k": 2.3060041352041667,
        "confidence": 0.95
      },
      "actual": {
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        "infinite": false,
        "k_source": "student_t"
      },
      "error_ulp": 486,
      "threshold_ulp": 0.000002,
      "ok": true
    },
    {
      "id": "o3-nu1",
      "kind": "student-t",
      "inputs": {
        "nu": 1,
        "confidence": 0.95
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "infinite": false,
        "k_source": "student_t",
        "nu": 1,
        "k": 12.706204736174705,
        "confidence": 0.95
      },
      "actual": {
        "k": 12.706204736174683,
        "confidence": 0.95,
        "nu": 1,
        "infinite": false,
        "k_source": "student_t"
      },
      "error_ulp": 12,
      "threshold_ulp": 0.000002,
      "ok": true
    },
    {
      "id": "o3-nu30",
      "kind": "student-t",
      "inputs": {
        "nu": 30,
        "confidence": 0.95
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "infinite": false,
        "k_source": "student_t",
        "nu": 30,
        "k": 2.042272456301238,
        "confidence": 0.95
      },
      "actual": {
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        "confidence": 0.95,
        "nu": 30,
        "infinite": false,
        "k_source": "student_t"
      },
      "error_ulp": 1258,
      "threshold_ulp": 0.000002,
      "ok": true
    },
    {
      "id": "o3-p99",
      "kind": "other-p",
      "inputs": {
        "nu": 8,
        "confidence": 0.99
      },
      "expected_f64": {
        "oracle_layer": "analytic",
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        "k_source": "student_t",
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        "k": 3.3553873313333953,
        "confidence": 0.99
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      "actual": {
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        "k_source": "student_t"
      },
      "error_ulp": 107,
      "threshold_ulp": 0.000002,
      "ok": true
    },
    {
      "id": "o3-alias",
      "kind": "alias",
      "inputs": {
        "nu_eff": 8,
        "confidence": 0.95
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "infinite": false,
        "k_source": "student_t",
        "nu": 8,
        "k": 2.3060041352041667,
        "confidence": 0.95
      },
      "actual": {
        "k": 2.306004135203951,
        "confidence": 0.95,
        "nu": 8,
        "infinite": false,
        "k_source": "student_t"
      },
      "error_ulp": 486,
      "threshold_ulp": 0.000002,
      "ok": true
    },
    {
      "id": "o3-nu2",
      "kind": "student-t",
      "inputs": {
        "nu": 2,
        "confidence": 0.95
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "infinite": false,
        "k_source": "student_t",
        "nu": 2,
        "k": 4.302652729749464,
        "confidence": 0.95
      },
      "actual": {
        "k": 4.302652729749459,
        "confidence": 0.95,
        "nu": 2,
        "infinite": false,
        "k_source": "student_t"
      },
      "error_ulp": 5,
      "threshold_ulp": 0.000002,
      "ok": true
    }
  ]
}