{
  "capability_id": "engineering.conformity.z_prime",
  "tool_id": "z-prime",
  "engine": "z-prime",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-15T23:38:12.907Z",
  "engine_build": "2026-09-15",
  "test_count": 12,
  "passed": 12,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 0,
      "passed": 0
    },
    "boundary": {
      "total": 7,
      "passed": 7
    },
    "property": {
      "total": 5,
      "passed": 5
    }
  },
  "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/z-prime",
  "api": "https://www.calculatorx.com/api/v1/calc/z-prime",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.conformity.z_prime.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.conformity.z_prime.output.json",
  "assumptions": [
    "ISO 13528 z′ = (ylab−xref)/√(σ_pt²+u(x_pt)²)",
    "σ_pt > 0 and u(x_pt) > 0 — u(x_pt)=0 is not a z-score wrap",
    "Not z-score, not zeta, and not En"
  ],
  "limitations": [
    "Requires σ_pt > 0 and u(x_pt) > 0 — this page does not wrap z-score",
    "Not the z-score (that divides by σ_pt alone)",
    "Not the zeta-score (that uses √(ulab²+uref²))",
    "Not the normalized error En (that uses already-expanded U)",
    "Not TUR and not an ILAC G8 specification decision on y"
  ],
  "boundary_conditions": [
    "missing ylab, xref, sigma, or u_xref → MISSING_REQUIRED_INPUT",
    "σ_pt ≤ 0 or u(x_pt) ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "ulab is not an alias for u_xref"
  ],
  "sources": [
    {
      "title": "ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison",
      "section": "z′ score when the uncertainty of the assigned value is not negligible",
      "supports": "z′ = (x − x_pt) / √(σ_pt² + u²(x_pt)). |z′| bands match the z-score bands.",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:8a4146e0f033dbfb0eeeb257bb898223288c8ec0d6d473d545e42ccd393f5b0a",
  "tests": [
    {
      "id": "boundary-zp",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "ylab": 5,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4
      },
      "expect": {
        "z_prime": 1,
        "abs_z_prime": 1,
        "denom": 5,
        "decision": "pass"
      },
      "expectWarning": null,
      "actual": {
        "z_prime": 1,
        "abs_z_prime": 1,
        "decision": "pass",
        "ylab": 5,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4,
        "denom": 5
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zp-two",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "ylab": 10,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4
      },
      "expect": {
        "z_prime": 2,
        "decision": "pass"
      },
      "expectWarning": null,
      "actual": {
        "z_prime": 2,
        "abs_z_prime": 2,
        "decision": "pass",
        "ylab": 10,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4,
        "denom": 5
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zp-warn",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "ylab": 12.5,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4
      },
      "expect": {
        "z_prime": 2.5,
        "decision": "warning"
      },
      "expectWarning": null,
      "actual": {
        "z_prime": 2.5,
        "abs_z_prime": 2.5,
        "decision": "warning",
        "ylab": 12.5,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4,
        "denom": 5
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zp-fail",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "ylab": 15,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4
      },
      "expect": {
        "z_prime": 3,
        "decision": "fail"
      },
      "expectWarning": null,
      "actual": {
        "z_prime": 3,
        "abs_z_prime": 3,
        "decision": "fail",
        "ylab": 15,
        "xref": 0,
        "sigma": 3,
        "u_xref": 4,
        "denom": 5
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zp-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "ylab": 5,
        "xref": 0,
        "sigma": 3
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "u_xref is required"
    },
    {
      "id": "boundary-zp-u",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "ylab": 5,
        "xref": 0,
        "sigma": 3,
        "u_xref": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "u_xref must be greater than zero"
    },
    {
      "id": "boundary-zp-ulab",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "ylab": 5,
        "xref": 0,
        "sigma": 3,
        "ulab": 4
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "u_xref is required"
    },
    {
      "id": "property-zp",
      "ok": true,
      "kind": "property",
      "detail": "1",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-zp-two",
      "ok": true,
      "kind": "property",
      "detail": "2",
      "expect": 2,
      "actual": 2
    },
    {
      "id": "property-zp-warn",
      "ok": true,
      "kind": "property",
      "detail": "warning",
      "expect": "warning",
      "actual": "warning"
    },
    {
      "id": "property-zp-fail",
      "ok": true,
      "kind": "property",
      "detail": "fail",
      "expect": "fail",
      "actual": "fail"
    },
    {
      "id": "property-zp-alias",
      "ok": true,
      "kind": "property",
      "detail": "1",
      "expect": 1,
      "actual": 1
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 12,
      "total": 12,
      "golden": 0,
      "boundary": 7,
      "property": 5
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-15T23:04:28.329Z",
  "rendered_at": "2026-09-15T23:38:12.907Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
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      "items": [
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        {
          "id": "schema-valid-input-executes",
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          "id": "engine-success-output-validates-schema",
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          "id": "schema-rejects-incomplete-input",
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    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
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}