{
  "capability_id": "engineering.process.capability",
  "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": "process-capability-mpmath-o3",
    "generator_version": "1.0.0",
    "generator_sha256": "80df2d3ceb3113c04163e5b5988635435f5fc64464beb63560d70cb31169ac6d",
    "table_sha256": "0bfecdd4b6d6cc36cdb828de51869e94b4b4057ec539f0efb09dae25d24b6c2d",
    "seed": "20260916.process-capability-o3",
    "independent_of_iut": true
  },
  "claim_scope": "O2: design-stage Cp/Cpk/Cpu/Cpl vs separate-module identities (≤2 ULP). Not Pp/Ppk, not Cpm, not P/T=1/Cp, not Monte Carlo, not an in-control SPC study. ≤2 ULP vs O3 applies only to the published tabulated Cp/Cpk vectors (centered, off-center, negative Cpk, aliases, σ=2, shifted limits, tight). It is not a whole-domain guarantee and does not cover Pp/Ppk, Cpm, P/T, or Monte Carlo simulated indices.",
  "commands": {
    "regenerate_table": "python3 generate-process-capability-o3.py",
    "regenerate_table_repo": "python3 scripts/lib/cvp/oracles/generate-process-capability-o3.py",
    "independent_rest": "Compare POST /api/v1/calc/process-capability against /developers/cvp/reproduce/process-capability-o3-tables.json",
    "run_cvp": "npm run cvp:run -- --capability engineering.process.capability",
    "rest_example": "POST https://www.calculatorx.com/api/v1/calc/process-capability"
  },
  "public_files": {
    "table": "/developers/cvp/reproduce/process-capability-o3-tables.json",
    "table_url": "https://www.calculatorx.com/developers/cvp/reproduce/process-capability-o3-tables.json",
    "generator": "/developers/cvp/reproduce/generate-process-capability-o3.py",
    "generator_url": "https://www.calculatorx.com/developers/cvp/reproduce/generate-process-capability-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.process.capability/1.0.0.cvp.json",
    "this_file": "/evidence/engineering.process.capability/reproduce.json"
  },
  "result_summary": {
    "passed": 8,
    "total": 8,
    "failed": 0,
    "max_error_ulp": 0,
    "threshold_ulp": 2,
    "max_threshold_ulp": 2
  },
  "vectors": [
    {
      "id": "o3-center",
      "kind": "centered",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 1
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 2,
        "Cpk": 2,
        "Cpu": 2,
        "Cpl": 2
      },
      "actual": {
        "Cp": 2,
        "Cpk": 2,
        "Cpu": 2,
        "Cpl": 2,
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 1
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-shift",
      "kind": "off-center-high",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 8,
        "sigma": 1
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 2,
        "Cpk": 1.3333333333333333,
        "Cpu": 1.3333333333333333,
        "Cpl": 2.6666666666666665
      },
      "actual": {
        "Cp": 2,
        "Cpk": 1.3333333333333333,
        "Cpu": 1.3333333333333333,
        "Cpl": 2.6666666666666665,
        "lsl": 0,
        "usl": 12,
        "mu": 8,
        "sigma": 1
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-shift-low",
      "kind": "off-center-low",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 4,
        "sigma": 1
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 2,
        "Cpk": 1.3333333333333333,
        "Cpu": 2.6666666666666665,
        "Cpl": 1.3333333333333333
      },
      "actual": {
        "Cp": 2,
        "Cpk": 1.3333333333333333,
        "Cpu": 2.6666666666666665,
        "Cpl": 1.3333333333333333,
        "lsl": 0,
        "usl": 12,
        "mu": 4,
        "sigma": 1
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sigma2",
      "kind": "centered-wider",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 2
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 1,
        "Cpk": 1,
        "Cpu": 1,
        "Cpl": 1
      },
      "actual": {
        "Cp": 1,
        "Cpk": 1,
        "Cpu": 1,
        "Cpl": 1,
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 2
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-unit",
      "kind": "shifted-limits",
      "inputs": {
        "lsl": 10,
        "usl": 16,
        "mu": 13,
        "sigma": 1
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 1,
        "Cpk": 1,
        "Cpu": 1,
        "Cpl": 1
      },
      "actual": {
        "Cp": 1,
        "Cpk": 1,
        "Cpu": 1,
        "Cpl": 1,
        "lsl": 10,
        "usl": 16,
        "mu": 13,
        "sigma": 1
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-neg",
      "kind": "negative-cpk",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 14,
        "sigma": 1
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 2,
        "Cpk": -0.6666666666666666,
        "Cpu": -0.6666666666666666,
        "Cpl": 4.666666666666667
      },
      "actual": {
        "Cp": 2,
        "Cpk": -0.6666666666666666,
        "Cpu": -0.6666666666666666,
        "Cpl": 4.666666666666667,
        "lsl": 0,
        "usl": 12,
        "mu": 14,
        "sigma": 1
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-alias",
      "kind": "alias",
      "inputs": {
        "LSL": 0,
        "USL": 12,
        "mean": 6,
        "std": 1
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 2,
        "Cpk": 2,
        "Cpu": 2,
        "Cpl": 2
      },
      "actual": {
        "Cp": 2,
        "Cpk": 2,
        "Cpu": 2,
        "Cpl": 2,
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 1
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-tight",
      "kind": "tight",
      "inputs": {
        "lsl": 0,
        "usl": 6,
        "mu": 3,
        "sigma": 0.5
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "Cp": 2,
        "Cpk": 2,
        "Cpu": 2,
        "Cpl": 2
      },
      "actual": {
        "Cp": 2,
        "Cpk": 2,
        "Cpu": 2,
        "Cpl": 2,
        "lsl": 0,
        "usl": 6,
        "mu": 3,
        "sigma": 0.5
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    }
  ]
}