{ "capability_id": "engineering.tolerance.monte_carlo", "tool_id": "monte-carlo-tolerance", "engine": "monte-carlo-tolerance", "calculation_version": "1.12.0", "generated_at": "2026-09-21T16:00:36.047Z", "engine_build": "2026-09-11", "test_count": 71, "passed": 71, "failed": 0, "tests_summary": { "golden": { "total": 5, "passed": 5 }, "boundary": { "total": 26, "passed": 26 }, "property": { "total": 40, "passed": 40 } }, "engine_tested": true, "expert_reviewed": false, "internally_reviewed": true, "review_kind": "internal", "source_checked": true, "reviewed_by": "CalculatorX tolerance / mechanical engineering review", "reviewer_role": "tolerance-engineer", "last_reviewed": "2026-08-12", "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 tolerance / mechanical engineering review", "role": "tolerance-engineer" }, "reviewed_at": "2026-08-12", "scope": [ "formula", "input semantics", "assumptions", "limitations", "sources", "tests" ], "kind": "internal" }, "page": "https://www.calculatorx.com/calc/engineering/monte-carlo-tolerance", "api": "https://www.calculatorx.com/api/v1/calc/monte-carlo-tolerance", "schema_input": "https://www.calculatorx.com/schemas/engineering.tolerance.monte_carlo.input.json", "schema_output": "https://www.calculatorx.com/schemas/engineering.tolerance.monte_carlo.output.json", "assumptions": [ "Independent unless correlations provided", "Correlated all-normal: joint two-piece normal via Cholesky", "Correlated non-normal: Gaussian-copula NORTA; entered ρ is latent Gaussian correlation, not Pearson of the finished marginals", "Cp*/Cpk* are design-stage simulated indices" ], "limitations": [ "1-D stack; correlations use joint normal (all-normal) or Gaussian-copula NORTA (non-normal marginals)", "Asymmetric normal uses two-piece scaling; uniform/triangular use [-tol_minus,+tol_plus]", "Cp/Cpk/Ppk are simulated design-stage indices from overall MC mean/σ — not measured in-control SPC", "Sobol requires independent inputs; for this linear stack Si=STi=analytic variance shares", "Shapley variance attribution supports correlation; exact for d≤12, permutation estimate for d>12", "Under NORTA, analytic σ uses Cov≈ρ·σi·σj (latent ρ); prefer Monte Carlo σ", "Shared query must encode noms/sense; legacy tol1/tol2 alone is error-only (nominals 0)", "Not full GD&T / 3-D geometry", "MCP/agent input schema is canonical (no legacy field aliases); REST still accepts aliases", "calculation_fingerprint is SHA-256; calculation_short_id is FNV-1a32 for UI only", "MCP execute/inspect default detail_level=summary; pass full for histogram/Sobol/Shapley/contributors", "Agent correlations use named pairs {a,b,rho} only (no i/j indexes)", "Agent tolerances: half_tolerance OR both tol_plus+tol_minus (no single-sided agent form)" ], 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Increase N or check SPEC_CENTER_MISMATCH." } ], "calculation_fingerprint": "sha256:e8100ffa92dbac1322cf561df8b535f75e2dadb46d36d48cc263f9320461b933", "calculation_short_id": "fnv1a32:3a8296b1", "rng": { "algorithm": "mulberry32", "normal_sampler": "box-muller", "version": "1.0", "seed": 1 }, "histogram": { "bins": 24, "min": -0.21173821212984065, "max": 0.21657675456860742, "counts": [ 2, 3, 2, 14, 10, 18, 16, 24, 35, 46, 44, 36, 49, 50, 41, 34, 26, 21, 10, 8, 3, 2, 3, 3 ] } }, "tol": 0 }, { "id": "property-seeded", "ok": true, "kind": "property", "detail": "deterministic", "expect": 0.07431402402418098, "actual": 0.07431402402418098 }, { "id": "property-std", "ok": true, "kind": "property", "detail": "std", "expect": 0.07431402402418098, "actual": 0.07431402402418098 }, { "id": "property-analytic", "ok": true, "kind": "property", "detail": "σ_analytic = √Σ(T/k)²", "expect": 0.07453559924999299, "actual": 0.07453559924999299 }, { "id": "property-mc-near-analytic", "ok": true, "kind": 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0.223606797749979 }, { "id": "property-100-tols", "ok": true, "kind": "property", "detail": "100 tolerances", "expect": 100, "actual": 100 }, { "id": "property-gap-nom", "ok": true, "kind": "property", "detail": "Gap A−B nominal+σ", "expect": { "stack_nom": 5, "std_analytic": 0.07453559924999299 }, "actual": { "stack_nom": 5, "std_analytic": 0.07453559924999299 } }, { "id": "property-yield", "ok": true, "kind": "property", "detail": "yield+Cp≥Cpk", "expect": { "yield": 0.99285, "Cp": 0.8983981967900372 }, "actual": { "yield": 0.99285, "ppm": 7150, "Cp": 0.8983981967900372, "Cpk": 0.893484684168217 } }, { "id": "property-corr-analytic", "ok": true, "kind": "property", "detail": "ρ=0.5 analytic σ = √(σ₁²+σ₂²+2ρσ₁σ₂)", "expect": 0.17320508075688773, "actual": 0.1732050807568877 }, { "id": "property-corr-mc-near-analytic", "ok": true, "kind": "property", "detail": "ρ=0.5 MC σ near analytic", "expect": { "analytic_expected": 0.17320508075688773, "relative_error_lt": 0.03 }, "actual": { "analytic_expected": 0.1732050807568877, "mc_observed": 0.17381471110713503, "relative_error": 0.0035197024682144637 } }, { "id": "property-mean-shift", "ok": true, "kind": "property", "detail": "mean_shift moves center", "expect": 5.1, "actual": 5.10142333581853 }, { "id": "property-sense-alias", "ok": true, "kind": "property", "detail": "sense/direction aliases", "expect": 5, "actual": 5 }, { "id": "property-uniform", "ok": true, "kind": "property", "detail": "uniform σ = T/√3", "expect": 0.17320508075688773, "actual": 0.17299254404663475 }, { "id": "property-triangular", "ok": true, "kind": "property", "detail": "triangular σ = T/√6", "expect": 1, "actual": 1.0024862940006003 }, { "id": "property-asym-mean", "ok": true, "kind": "property", "detail": "asymmetric uniform E[ε]=(+−)/2", "expect": 0.075, "actual": 0.07520854572218731 }, { "id": "property-sensitivity", "ok": true, "kind": "property", "detail": "Spearman |ρ|≤1", "expect": true, "actual": [ 0.43122055780513946, 0.8842987595746898 ] }, { "id": "property-convergence-meta", "ok": true, "kind": "property", "detail": "convergence checkpoints", "expect": { "N": [ 100, 2000 ] }, "actual": [ 100, 1000, 2000 ] }, { "id": "property-pearson", "ok": true, "kind": "property", "detail": "Pearson sensitivity lock", "expect": 0.4384760734091528, "actual": 0.4384760734091528 }, { "id": "property-spec-mismatch-warn", "ok": true, "kind": "property", "detail": "SPEC_CENTER_MISMATCH when center outside LSL/USL", "expect": "SPEC_CENTER_MISMATCH", "actual": "SPEC_CENTER_MISMATCH" }, { "id": "property-gap-no-mismatch", "ok": true, "kind": "property", "detail": "aligned gap stack has no SPEC_CENTER_MISMATCH", "expect": false, "actual": [] }, { "id": "property-yield-extreme-warn", "ok": true, "kind": "property", "detail": "YIELD_SAMPLING_EXTREME + rule of three when 0 passes", "expect": 0.006, "actual": 0.006 }, { "id": "property-fingerprint", "ok": true, "kind": "property", "detail": "SHA-256 calculation_fingerprint + FNV short_id lock", "expect": { "fingerprint": "sha256:…", "short_id": "fnv1a32:becf725e" }, "actual": { "fingerprint": "sha256:137b9bac0d4c6f3e655eb04ce9450c62296e02e564dec2d43bddb74ef8105658", "short_id": "fnv1a32:becf725e" } }, { "id": "property-sobol-exact", "ok": true, "kind": "property", "detail": "Sobol Si=STi=variance share", "expect": { "Si": [ 0.2, 0.8 ] }, "actual": [ 0.19999999999999998, 0.7999999999999999 ] }, { "id": "property-shapley-indep", "ok": true, "kind": "property", "detail": "Shapley independent = Sobol shares", "expect": { "shares": [ 0.2, 0.8 ] }, "actual": [ 0.20000000000000004, 0.7999999999999999 ] }, { "id": "property-shapley-corr", "ok": true, "kind": "property", "detail": "Shapley correlated shares sum≈1", "expect": 1, "actual": 0.9999999999999999 }, { "id": "property-norta", "ok": true, "kind": "property", "detail": "NORTA uniform+ρ · MC σ near analytic approx", "expect": { "model": "gaussian_copula_norta", "rel_lt": 0.03 }, "actual": { "model": "gaussian_copula_norta", "rel": -0.00440125025153823, "warn": [ "CORRELATED_NORTA" ] } }, { "id": "property-share-url-noms", "ok": true, "kind": "property", "detail": "Shared URL noms/sense → gap yield + Wilson CI", "expect": { "stack_nom": 5, "yield": 0.9935, "ci": "wilson" }, "actual": { "stack_nom": 5, "yield": 0.9935, "ci": [ 0.9889104708274775, 0.9961974035059259 ] } }, { "id": "property-legacy-tol-nom0", "ok": true, "kind": "property", "detail": "Legacy tol1/tol2+spec without noms → nom=0 (no client invention)", "expect": { "stack_nom": 0, "yield": 0 }, "actual": { "stack_nom": 0, "yield": 0 } }, { "id": "property-parity-fingerprint", "ok": true, "kind": "property", "detail": "Canonical tolerances[] ↔ legacy query inputs → same fingerprint", "expect": { "fp": "sha256:dc088ad8eef4b8b91947a2ac4c3e174dd92a07e46bc98c4fa7b734ac84df3431", "yield": 0.9935 }, "actual": { "fp_canon": "sha256:dc088ad8eef4b8b91947a2ac4c3e174dd92a07e46bc98c4fa7b734ac84df3431", "fp_legacy": "sha256:dc088ad8eef4b8b91947a2ac4c3e174dd92a07e46bc98c4fa7b734ac84df3431", "yield": [ 0.9935, 0.9935 ] } }, { "id": "property-fingerprint-stable", "ok": true, "kind": "property", "detail": "Identical request → identical SHA-256 fingerprint", "expect": "sha256:dc088ad8eef4b8b91947a2ac4c3e174dd92a07e46bc98c4fa7b734ac84df3431", "actual": "sha256:dc088ad8eef4b8b91947a2ac4c3e174dd92a07e46bc98c4fa7b734ac84df3431" }, { "id": "property-mcp-summary-fields", "ok": true, "kind": "property", "detail": "Summary contract fields present on engine result", "expect": [ "stack_center", "mean", "std", "yield", "reject_rate", "simulated_Cpk", "warnings", "calculation_fingerprint" ], "actual": [ "stack_center", "mean", "std", "yield", "reject_rate", "simulated_Cpk", "warnings", "calculation_fingerprint" ] } ], "tier": "internally_reviewed", "verification": { "tests": { "passed": 71, "total": 71, "golden": 5, "boundary": 26, "property": 40 }, "contract_checks": { "passed": 10, "total": 10 } }, "evidence_core_generated_at": "2026-09-11T23:04:52.544Z", "rendered_at": "2026-09-21T16:00:36.047Z", "release_integrity": { "status": "verified", "scope": "workspace", "production_attestation_required": true, "calculation_version": "1.12.0", "artifacts": { "engine": "1.12.0", "page": "1.12.0", "capability": "1.12.0", "evidence": "1.12.0", "input_schema": "1.12.0", "output_schema": "1.12.0", "mcp_contract": "1.12.0" }, "digests": { "input_schema_sha256": "55ee91bbeba09c82e0effc6d2c3bf95a9e0d7afe24f8b056bf217788b81992b1", "output_schema_sha256": "6bd4d91cb24648c1c65224651fb3153e3b3c7149b5328f5362df59d0ec62744a", "evidence_sha256": "30a8f1ad6fe3df4af69da2a2ac605ea9c8e05793f23b1d5465828c15cb5c9c68", "evidence_core_sha256": "30a8f1ad6fe3df4af69da2a2ac605ea9c8e05793f23b1d5465828c15cb5c9c68", "capability_sha256": "396dd6ff9f32fa630246c302a98c29c5c8fb0a151a475c86d4954d30cc7c86c7", "engine_sha256": "925bd3b9c373f747a10f30cedc6352b3f419cf91144ae6744c9c9adcd703033c", "mcp_contract_sha256": "2bb4bbc15ea3f9842a9a464e07efcc692dc31f3e830dee8553f3d7c4e81238d3" }, "contract_checks": { "total": 10, "passed": 10, "failed": 0, "items": [ { "id": "contract-page-version", "status": "pass", "detail": "1.12.0" }, { "id": "contract-capability-version", "status": "pass", "detail": "1.12.0" }, { "id": "contract-input-schema-version", "status": "pass", "detail": "1.12.0" }, { "id": "contract-output-schema-version", "status": "pass", "detail": "1.12.0" }, { "id": "evidence-version-matches-manifest", "status": "pass", "detail": "1.12.0" }, { "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" } }