{
  "capability_id": "engineering.uncertainty.welch_satterthwaite",
  "tool_id": "welch-satterthwaite",
  "engine": "welch-satterthwaite",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:03:43.734Z",
  "engine_build": "2026-09-15",
  "test_count": 10,
  "passed": 10,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 0,
      "passed": 0
    },
    "boundary": {
      "total": 6,
      "passed": 6
    },
    "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/welch-satterthwaite",
  "api": "https://www.calculatorx.com/api/v1/calc/welch-satterthwaite",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.uncertainty.welch_satterthwaite.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.uncertainty.welch_satterthwaite.output.json",
  "assumptions": [
    "JCGM 100:2008 G.4 Welch–Satterthwaite",
    "If uc omitted, u_c = RSS of uncorrelated u_i",
    "Infinite ν_i contribute 0 to the sum",
    "Not GUM model combination and not expanded U = k·u_c"
  ],
  "limitations": [
    "Does not combine a measurement model (use Uncertainty propagate)",
    "Does not look up coverage factor k from a t-table",
    "Does not compute expanded U = k·u_c",
    "Uncorrelated RSS only when uc is omitted"
  ],
  "boundary_conditions": [
    "missing u or nu → MISSING_REQUIRED_INPUT",
    "length mismatch → INVALID_INPUT",
    "u_c = 0 → VALUE_MUST_BE_POSITIVE",
    "ν_i ≤ 0 and not inf → VALUE_MUST_BE_POSITIVE"
  ],
  "sources": [
    {
      "title": "JCGM 100:2008 (GUM) — Evaluation of measurement data",
      "section": "G.4 Effective degrees of freedom: the Welch–Satterthwaite formula",
      "url": "https://www.bipm.org/en/committees/jc/jcgm/publications",
      "supports": "ν_eff = u_c⁴ / Σ (u_i⁴ / ν_i) for the coverage factor of expanded uncertainty",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:d609c74a6215dbd2f95f8c688ec955a44fb1b1722e4990703a23d2858b3d5ea7",
  "tests": [
    {
      "id": "boundary-ws",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "u": [
          1,
          1
        ],
        "nu": [
          8,
          8
        ]
      },
      "expect": {
        "nu_eff": 16,
        "uc": 1.4142135623730951,
        "infinite": false
      },
      "expectWarning": null,
      "actual": {
        "nu_eff": 16,
        "infinite": false,
        "uc": 1.4142135623730951,
        "u": [
          1,
          1
        ],
        "nu": [
          8,
          8
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ws-inf",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "u": [
          0.1,
          0.2
        ],
        "nu": [
          10,
          "inf"
        ]
      },
      "expect": {
        "nu_eff": 250,
        "infinite": false
      },
      "expectWarning": null,
      "actual": {
        "nu_eff": 250,
        "infinite": false,
        "uc": 0.223606797749979,
        "u": [
          0.1,
          0.2
        ],
        "nu": [
          10,
          null
        ]
      },
      "tol": 1e-9
    },
    {
      "id": "boundary-ws-all-inf",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "u": [
          1,
          2
        ],
        "nu": [
          "inf",
          "inf"
        ]
      },
      "expect": {
        "nu_eff": null,
        "infinite": true
      },
      "expectWarning": null,
      "actual": {
        "nu_eff": null,
        "infinite": true,
        "uc": 2.23606797749979,
        "u": [
          1,
          2
        ],
        "nu": [
          null,
          null
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ws-len",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "u": [
          1,
          1
        ],
        "nu": [
          8
        ]
      },
      "expectError": "INVALID_INPUT",
      "code": "INVALID_INPUT",
      "error": "u and nu must have the same length"
    },
    {
      "id": "boundary-ws-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "u": [
          0,
          0
        ],
        "nu": [
          8,
          8
        ]
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "uc must be greater than zero"
    },
    {
      "id": "boundary-ws-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "u": [
          1,
          1
        ]
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "nu is required"
    },
    {
      "id": "property-ws-equal",
      "ok": true,
      "kind": "property",
      "detail": "16",
      "expect": 16,
      "actual": 16
    },
    {
      "id": "property-ws-uc",
      "ok": true,
      "kind": "property",
      "detail": "√2",
      "expect": 1.4142135623730951,
      "actual": 1.4142135623730951
    },
    {
      "id": "property-ws-typeb-inf",
      "ok": true,
      "kind": "property",
      "detail": "250",
      "expect": 250,
      "actual": 250
    },
    {
      "id": "property-ws-infinite",
      "ok": true,
      "kind": "property",
      "detail": "infinite",
      "expect": true,
      "actual": true
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 10,
      "total": 10,
      "golden": 0,
      "boundary": 6,
      "property": 4
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-15T07:59:57.695Z",
  "rendered_at": "2026-09-16T22:03:43.734Z",
  "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": "eac919d25af450aeab502496247f636d0654dd754cee4037898e741cba00d856",
      "output_schema_sha256": "91c22db74bd4b74afc6434847efcfa44328831d784e03c1253897753af369b9c",
      "evidence_sha256": "507b5c9086c10801a9c5b1bd0ef85e65277196f816ad9a608360cda2f6db87db",
      "evidence_core_sha256": "507b5c9086c10801a9c5b1bd0ef85e65277196f816ad9a608360cda2f6db87db",
      "capability_sha256": "f4534e45537524c3a8094117c8316c8dbf9f82398b6817346394dad126047e52",
      "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"
  }
}
