{
  "capability_id": "engineering.uncertainty.weighted_mean",
  "tool_id": "weighted-mean",
  "engine": "weighted-mean",
  "calculation_version": "1.0.1",
  "generated_at": "2026-10-22T08:54:34.768Z",
  "engine_build": "2026-09-23",
  "test_count": 9,
  "passed": 9,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 1,
      "total": 1
    },
    "boundary": {
      "passed": 5,
      "total": 5
    },
    "property": {
      "passed": 3,
      "total": 3
    }
  },
  "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/weighted-mean",
  "api": "https://www.calculatorx.com/api/v1/calc/weighted-mean",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.uncertainty.weighted_mean.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.uncertainty.weighted_mean.output.json",
  "assumptions": [
    "JCGM 100:2008 H.3 inverse-variance weighted mean of independent uncorrelated results of the same measurand",
    "Each u_i is a standard uncertainty greater than zero",
    "Not combined RSS, not Type A u_A = s/√n, and not GUM propagate",
    "χ² / Birge are diagnostics, not a pass/fail"
  ],
  "limitations": [
    "Independent uncorrelated results of the same measurand — not RSS of a measurement model",
    "Does not compute Type A u_A = s/√n from repeats without individual u_i",
    "Does not compute expanded U = k·u_w",
    "χ² / Birge are diagnostics, not a pass/fail verdict"
  ],
  "boundary_conditions": [
    "missing x or u → MISSING_REQUIRED_INPUT",
    "length mismatch → INVALID_INPUT",
    "any u_i ≤ 0 → VALUE_MUST_BE_POSITIVE"
  ],
  "sources": [
    {
      "title": "JCGM 100:2008 — Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM)",
      "section": "H.3 Measurements sampled from a distribution: weighted mean",
      "url": "https://www.bipm.org/en/publications/guides/gum.html",
      "supports": "x_w = Σ(x_i/u²(x_i))/Σ(1/u²(x_i)); u²(x_w) = 1/Σ(1/u²(x_i)) for independent uncorrelated results of the same measurand",
      "kind": "standard"
    },
    {
      "title": "JCGM 100:2008 — Combined standard uncertainty (RSS of a measurement model)",
      "section": "5.1.2 uncorrelated input quantities",
      "supports": "RSS u_c = √Σ (c_i u_i)² is a different contract; this page does not combine a measurement model",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:fba713ade5bb42da5de3ab874d710f916eb663100287fb35102725987ee0740d",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 9,
      "total": 9,
      "golden": 1,
      "boundary": 5,
      "property": 3
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-23T09:08:38.031Z",
  "rendered_at": "2026-10-22T08:54:34.768Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.1",
    "artifacts": {
      "engine": "1.0.1",
      "page": "1.0.1",
      "capability": "1.0.1",
      "evidence": "1.0.1",
      "input_schema": "1.0.1",
      "output_schema": "1.0.1",
      "mcp_contract": "1.0.1"
    },
    "digests": {
      "input_schema_sha256": "da008f579c37f7c7c08cd298509b622dfe4ee81c41ed32349e926b804c153c47",
      "output_schema_sha256": "d2629b5ce5875b7414b46d84e47b0e0793e4e7c060d9f4e49b8747c6cd45997d",
      "evidence_sha256": "2499c222f5eea21ae0c95c9f3cd10e4ddca9f85bd870b2c604d8571c96ff4fee",
      "evidence_core_sha256": "2499c222f5eea21ae0c95c9f3cd10e4ddca9f85bd870b2c604d8571c96ff4fee",
      "capability_sha256": "41fec6d567265863aff2193280cac3b6127bc2f91139e4984516b9855e540d7a",
      "engine_sha256": "a664ae25cd2134de7de43a99352933043215473589aec38c9416508150cb1008",
      "mcp_contract_sha256": "a1a8617719bef45391ee6917dc1783a01de2eedf297e7596b3cb5017cd0e1560"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.1"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "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"
  }
}