{ "capability_id": "engineering.uncertainty.propagate", "tool_id": "uncertainty-propagate", "engine": "uncertainty-propagate", "calculation_version": "1.9.8", "generated_at": "2026-09-16T22:03:43.714Z", "engine_build": "2026-09-12", "test_count": 88, "passed": 88, "failed": 0, "tests_summary": { "golden": { "total": 11, "passed": 11 }, "boundary": { "total": 48, "passed": 48 }, "property": { "total": 29, "passed": 29 } }, "engine_tested": true, "expert_reviewed": false, "internally_reviewed": true, "review_kind": "internal", "source_checked": true, "reviewed_by": "CalculatorX engineering review", "reviewer_role": "metrology-engineer", "last_reviewed": "2026-08-10", "expert_review": { "status": "not_applicable", "reviewer": null, "note": "Internal domain review completed; not a named external expert review.", "kind": "internal" }, "internal_review": { "status": "approved", "reviewer": { "name": "CalculatorX engineering review", "role": "metrology-engineer" }, "reviewed_at": "2026-08-10", "scope": [ "formula", "input semantics", "assumptions", "limitations", "sources", "tests" ], "kind": "internal" }, "page": "https://www.calculatorx.com/calc/engineering/uncertainty-propagate", "api": "https://www.calculatorx.com/api/v1/calc/uncertainty-propagate", "schema_input": "https://www.calculatorx.com/schemas/engineering.uncertainty.propagate.input.json", "schema_output": "https://www.calculatorx.com/schemas/engineering.uncertainty.propagate.output.json", "assumptions": [ "Default uncorrelated (rho=0); optional correlations when provided.", "Linear propagation assumes a local first-order approximation is adequate. For significant model nonlinearity, consider higher-order treatment (JCGM 100:2008/Amd.1:2026) or Monte Carlo propagation (JCGM 101:2008)." ], "limitations": [ "Linear GUM (binary/sensitivity/RSS/budget) or Monte Carlo (JCGM 101) with normal/rectangular draws; not adaptive/MCMC", "MC: N in 100…100000 (default 10000), deterministic Mulberry32 seed; confidence → empirical percentiles; k → U=k·u_c", "budget/sensitivity Type A/B + distributions are metadata (except MC uses distribution for draws); u is standard uncertainty", "contributions are diagonal (c·u)² fractions for linear modes; with correlations percents may not sum to 100%", "Product/quotient use absolute first-order forms in linear mode; MC quotient rejects >5% near-zero denominator draws (MONTECARLO_UNSTABLE)", "n×n correlation matrix not positive semidefinite → CORRELATION_MATRIX_NOT_PSD (singular PSD allowed); duplicate unordered pair → DUPLICATE_CORRELATION; conflicting ρ for the same pair → CONFLICTING_CORRELATION", "Optional Quantity Engine v1.1: SI-prefix conversion + electrical derived rewrites (1000 mV + 2 V → 3 V; V/A → Ω; A·Ω → V; V×A → VA); different additive dimensions → UNIT_MISMATCH; not full SI algebra", "Unknown mode → INVALID_MODE; k and confidence together → INVALID_INPUT", "confidence with nonzero ρ/correlations → CORRELATED_DOF_NOT_SUPPORTED (use fixed k)", "MC rectangular + correlation → CORRELATED_NON_NORMAL_MC_NOT_SUPPORTED (normal marginals only)", "Public Agent schema uses canonical field names only (components.u/c/x; correlations i/j as index or name). Runtime still accepts legacy aliases (ua/uncertainty/sensitivity/value) for compatibility." ], "boundary_conditions": [ "Missing required fields → MISSING_REQUIRED_INPUT", "Negative ua/ub → VALUE_MUST_BE_NON_NEGATIVE", "Unknown mode → INVALID_MODE", "Quotient with b=0 → DIVISION_BY_ZERO", "Product with a=0 or b=0 is allowed (absolute form); u_rel omitted when y=0", "sum/difference with unit_a ≠ unit_b → UNIT_MISMATCH", "rho ∉ [-1,1] → VALUE_OUT_OF_RANGE; k≤0 → VALUE_MUST_BE_POSITIVE", "RSS with correlations → INVALID_INPUT", "confidence with nonzero ρ/correlations → CORRELATED_DOF_NOT_SUPPORTED", "Monte Carlo rectangular + correlation → CORRELATED_NON_NORMAL_MC_NOT_SUPPORTED", "Monte Carlo quotient with >5% near-zero denominator draws → MONTECARLO_UNSTABLE", "n×n correlation matrix not positive semidefinite → CORRELATION_MATRIX_NOT_PSD (pairwise |ρ|≤1 is not sufficient for 3+ variables; singular PSD is allowed)", "Duplicate unordered (i,j) pair → DUPLICATE_CORRELATION; conflicting ρ for the same pair → CONFLICTING_CORRELATION" ], "sources": [ { "title": "JCGM 100:2008 — Evaluation of measurement data (GUM)", "section": "Law of propagation of uncertainty", "url": "https://www.bipm.org/en/committees/jc/jcgm/publications", "supports": "u_c² = Σ (∂f/∂xᵢ)² u²(xᵢ) for uncorrelated inputs", "kind": "standard" }, { "title": "JCGM 100:2008/Amd.1:2026 — Nonlinearity in measurement models", "section": "Amendment 1", "url": "https://www.bipm.org/en/committees/jc/jcgm/publications", "supports": "First-order linear propagation may be inadequate when the measurement model is significantly nonlinear", "kind": "standard" }, { "title": "JCGM GUM-6:2020 — Developing and using measurement models", "section": "Measurement modelling", "url": "https://www.bipm.org/en/committees/jc/jcgm/publications", "supports": "Guidance on constructing measurement models for uncertainty evaluation", "kind": "standard" }, { "title": "JCGM 101:2008 — Propagation of distributions using a Monte Carlo method", "section": "GUM Supplement 1", "url": "https://www.bipm.org/en/committees/jc/jcgm/publications", "supports": "Methodological reference for the implemented Monte Carlo subset (normal/rectangular, seeded sampling, percentile intervals); not adaptive MCM, arbitrary PDFs, or full JCGM 101 validation procedure", "kind": "standard" }, { "title": "NIST Technical Note 1297", "section": "Guidelines for evaluating and expressing uncertainty", "url": "https://www.nist.gov/pml/nist-technical-note-1297", "supports": "Combined standard uncertainty practice; reporting of u_c", "kind": "reference" }, { "title": "NIST Guide to the SI (SP 811)", "section": "Expression of uncertainty with SI quantities", "url": "https://www.nist.gov/pml/special-publication-811", "supports": "Unit-consistent reporting of results and uncertainties", "kind": "reference" } ], "methods": [], "fingerprint": "sha256:d8cfcf55210b3e57585f02738f49bb344b4c1cc9d6597384fadb8f7da98e3fb8", "tests": [ { "id": "sum-default", 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"actual": 150 }, { "id": "property-sum-u", "ok": true, "kind": "property", "detail": "u=√(ua²+ub²)", "expect": 0.22360679774997896, "actual": 0.223606797749979 }, { "id": "property-diff-u", "ok": true, "kind": "property", "detail": "diff shares RSS u", "expect": 0.223606797749979, "actual": 0.223606797749979 }, { "id": "property-product", "ok": true, "kind": "property", "detail": "product absolute first-order", "expect": { "y": 50, "u_c": 0.7071067811865476 }, "actual": { "mode": "product", "y": 50, "u_c": 0.7071067811865476, "u_rel": 0.01414213562373095, "a": 10, "b": 5, "ua": 0.1, "ub": 0.05, "rho": 0, "nua": null, "nub": null, "unit": null, "unit_a": null, "unit_b": null, "contributions": [ { "i": 0, "label": "a", "c": 5, "u": 0.1, "variance": 0.25, "percent": 49.999999999999986, "type": null, "nu": null }, { "i": 1, "label": "b", "c": 10, "u": 0.05, "variance": 0.25, "percent": 49.999999999999986, "type": null, "nu": null } ], "covariance_contributions": [], "largest": { "i": 0, "label": "a", "percent": 49.999999999999986 }, "nu_eff": null, "nu_eff_infinite": false, "k": null, "U": null, "k_source": null, "confidence": null, "reported": { "u_c": 0.71, "y": 50, "significant_digits": 2, "decimal_places": 2, "formatted_u_c": "0.71", "formatted_y": "50.00" } } }, { "id": "property-product-a-zero", "ok": true, "kind": "property", "detail": "product a=0 → y=0, u_c=|b|ua, u_rel null", "expect": { "y": 0, "u_c": 0.5, "u_rel": null }, "actual": { "mode": "product", "y": 0, "u_c": 0.5, "u_rel": null, "a": 0, "b": 5, "ua": 0.1, "ub": 0.05, "rho": 0, "nua": null, "nub": null, "unit": null, "unit_a": null, "unit_b": null, "contributions": [ { "i": 0, "label": "a", "c": 5, "u": 0.1, "variance": 0.25, "percent": 100, "type": null, "nu": null }, { "i": 1, "label": "b", "c": 0, "u": 0.05, "variance": 0, "percent": 0, "type": null, "nu": null } ], "covariance_contributions": [], "largest": { "i": 0, "label": "a", "percent": 100 }, "nu_eff": null, "nu_eff_infinite": false, "k": null, "U": null, "k_source": null, "confidence": null, "reported": { "u_c": 0.5, "y": 0, "significant_digits": 2, "decimal_places": 2, "formatted_u_c": "0.50", "formatted_y": "0.00" } } }, { "id": "property-quotient-a-zero", "ok": true, "kind": "property", "detail": "quotient a=0 → u_c=|ua/b|, u_rel null", "expect": { "y": 0, "u_c": 0.02, "u_rel": null }, "actual": { "mode": "quotient", "y": 0, "u_c": 0.020000000000000004, "u_rel": null, "a": 0, "b": 5, "ua": 0.1, "ub": 0.05, "rho": 0, "nua": null, "nub": null, "unit": null, "unit_a": null, "unit_b": null, "contributions": [ { "i": 0, "label": "a", "c": 0.2, "u": 0.1, "variance": 0.0004000000000000002, "percent": 100.00000000000001, "type": null, "nu": null }, { "i": 1, "label": "b", "c": 0, "u": 0.05, "variance": 0, "percent": 0, "type": null, "nu": null } ], "covariance_contributions": [], "largest": { "i": 0, "label": "a", "percent": 100.00000000000001 }, "nu_eff": null, "nu_eff_infinite": false, "k": null, "U": null, "k_source": null, "confidence": null, "reported": { "u_c": 0.02, "y": 0, "significant_digits": 2, "decimal_places": 3, "formatted_u_c": "0.020", "formatted_y": "0.000" } } }, { "id": "property-quotient-b-zero", "ok": true, "kind": "property", "detail": "quotient b=0 → DIVISION_BY_ZERO", "expect": "DIVISION_BY_ZERO", "actual": true }, { "id": "property-sens", "ok": true, "kind": "property", "detail": "√Σ(c·u)²", "expect": 0.6324555320336759, "actual": 0.632455532033676 }, { "id": "property-rss", "ok": true, "kind": "property", "detail": "3-4-5 RSS", "expect": 0.5, "actual": 0.5 }, { "id": "property-zero-u", "ok": true, "kind": "property", "detail": "all ua=0 → u_c=0", "expect": 0, "actual": 0 }, { "id": "property-reported", "ok": true, "kind": "property", "detail": "reported u_c=0.22 (2 sig) with formatted_y=150.00; raw retained", "expect": { "reported_u_c": 0.22, "formatted_y": "150.00", "raw": 0.22360679774997896 }, "actual": { "u_c": 0.22, "y": 150, "significant_digits": 2, "decimal_places": 2, "formatted_u_c": "0.22", "formatted_y": "150.00" } }, { "id": "property-unit-match", "ok": true, "kind": "property", "detail": "matching units → V", "expect": "V", "actual": "V" }, { "id": "property-unit-mismatch", "ok": true, "kind": "property", "detail": "V+A → UNIT_MISMATCH", "expect": "UNIT_MISMATCH", "actual": true }, { "id": "property-unit-si-prefix", "ok": true, "kind": "property", "detail": "1000 mV + 2 V → 3 V", "expect": { "y": 3, "unit": "V" }, "actual": { "y": 3, "unit": "V", "converted": true } }, { "id": "property-unit-product", "ok": true, "kind": "property", "detail": "product units → VA", "expect": "VA", "actual": "VA" }, { "id": "property-unit-ohm", "ok": true, "kind": "property", "detail": "V/A → Ω", "expect": { "y": 5, "unit": "Ω" }, "actual": { "y": 5, "unit": "Ω" } }, { "id": "property-unit-mv-ma", "ok": true, "kind": "property", "detail": "mV/mA → Ω after SI convert", "expect": { "y": 500, "unit": "Ω" }, "actual": { "y": 500, "unit": "Ω" } }, { "id": "property-rho-perfect", "ok": true, "kind": "property", "detail": "sum ρ=1 → ua+ub", "expect": 0.3, "actual": 0.30000000000000004 }, { "id": "property-rho-anti", "ok": true, "kind": "property", "detail": "sum ρ=−1 → |ua−ub|", "expect": 0.1, "actual": 0.1 }, { "id": "property-expanded-U", "ok": true, "kind": "property", "detail": "U=k·u_c with reported.U", "expect": { "U": 0.4472135954999579, "reported_U": 0.45 }, "actual": { "U": 0.447213595499958, "reported_U": 0.45 } }, { "id": "property-sens-rho0", "ok": true, "kind": "property", "detail": "sensitivity ρ=0 matches uncorrelated", "expect": 0.6324555320336759, "actual": 0.632455532033676 }, { "id": "property-contrib", "ok": true, "kind": "property", "detail": "ub dominates → 80%", "expect": { "p0": 20, "p1": 80, "largest": 1 }, "actual": { "p0": 20, "p1": 80, "largest": 1 } }, { "id": "property-nueff", "ok": true, "kind": "property", "detail": "WS νeff with νb→∞", "expect": 225, "actual": 225.00000000000003 }, { "id": "property-types", "ok": true, "kind": "property", "detail": "Type A/B + labels pass-through", "expect": { "type": "A", "label": "y" }, "actual": { "type": "A", "label": "y" } }, { "id": "property-student-t", "ok": true, "kind": "property", "detail": "Student-t k(ν=9, p=0.95)", "expect": { "k": 2.26215716274, "source": "student_t" }, "actual": { "k": 2.2621571627981485, "source": "student_t" } }, { "id": "property-budget", "ok": true, "kind": "property", "detail": "budget y=Σx, Vref largest", "expect": { "y": 5, "largest": "Vref" }, "actual": { "y": 5, "largest": "Vref" } }, { "id": "property-mc-sum", "ok": true, "kind": "property", "detail": "MC sum ≈ linear u_c within 3%", "expect": { "linear": 0.22360679774997896 }, "actual": { "u_c": 0.22374005459107515, "y": 149.99808687493373 } }, { "id": "property-corr-singular-psd", "ok": true, "kind": "property", "detail": "all ρ=1 3×3 → u_c=0.3", "expect": 0.3, "actual": 0.30000000000000004 }, { "id": "property-corr-not-psd", "ok": true, "kind": "property", "detail": "pairwise |ρ|≤1 but non-PSD 3×3 → CORRELATION_MATRIX_NOT_PSD", "expect": "CORRELATION_MATRIX_NOT_PSD", "actual": true } ], "tier": "internally_reviewed", "verification": { "tests": { "passed": 88, "total": 88, "golden": 11, "boundary": 48, "property": 29 }, "contract_checks": { "passed": 8, "total": 8 } }, "evidence_core_generated_at": "2026-09-12T08:32:37.705Z", "rendered_at": "2026-09-16T22:03:43.714Z", "release_integrity": { "status": "verified", "scope": "workspace", "production_attestation_required": true, "calculation_version": "1.9.8", "artifacts": { "engine": "1.9.8", "page": "1.9.8", "capability": "1.9.8", "evidence": "1.9.8", "input_schema": "1.9.8", "output_schema": "1.9.8", "mcp_contract": "1.9.8" }, "digests": { "input_schema_sha256": "263d0ba0dda3ea81aa635bcd61d0eb9e9e9fc347ab4890b6cc20ccacc3a6843f", "output_schema_sha256": "d1d0c1d06cbe6b38725a8566ba4273291b9558081c5786b8e0b65b862a8e66b1", "evidence_sha256": 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"status": "pass" }, { "id": "schema-rejects-incomplete-input", "status": "pass" } ] }, "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json" } }