{
  "capability_id": "engineering.tolerance.stackup",
  "tool_id": "tolerance-stackup",
  "engine": "tolerance-stackup",
  "calculation_version": "1.4.0",
  "generated_at": "2026-09-16T22:03:43.725Z",
  "engine_build": "2026-09-11",
  "test_count": 35,
  "passed": 35,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 4,
      "passed": 4
    },
    "boundary": {
      "total": 13,
      "passed": 13
    },
    "property": {
      "total": 18,
      "passed": 18
    }
  },
  "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": "2026-08-11",
  "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": "2026-08-11",
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "kind": "internal"
  },
  "page": "https://www.calculatorx.com/calc/engineering/tolerance-stackup",
  "api": "https://www.calculatorx.com/api/v1/calc/tolerance-stackup",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.tolerance.stackup.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.tolerance.stackup.output.json",
  "assumptions": [
    "Linear 1-D stack",
    "All contributors must use the same unit. CalculatorX performs no implicit unit conversion; mixed-unit input is unsupported",
    "Basic mode: signs ignored via |tol|",
    "Engineering: direction + adds / − subtracts; asymmetric ±tol supported",
    "RSS assumes independent contributors",
    "Default statistical_basis=magnitude → u=a with no coverage probability",
    "1sigma → u=a; 3sigma → u=a/3; uniform → u=a/√3",
    "Uniform asymmetric ±tol: statistical center uses interval midpoint; stack_nom stays drawing nominal",
    "Legacy distribution=normal→1sigma, unknown→magnitude, uniform→uniform",
    "stack_half_range ≠ stack_worst when +Tol/−Tol are asymmetric about nominal",
    "When inputs are specification limits rather than σ-based values, prefer magnitude — RSS is an estimate and not a guaranteed assembly limit"
  ],
  "limitations": [
    "1-D linear stack only — not geometric GD&T or Monte Carlo",
    "Basic inputs are treated as comparable tolerance magnitudes, not automatically as 1σ / 3σ / drawing limits",
    "RSS is a statistical estimate under independence; it is not a guaranteed assembly limit",
    "Engineering statistical_basis: magnitude (default, no coverage) and 1sigma use a; 3sigma uses a/3; uniform uses a/√3",
    "Uniform asymmetric ±tol shifts statistical center to interval midpoint (NIST Type B rectangular); stack_nom stays drawing nominal",
    "Legacy distribution=normal→1sigma, unknown→magnitude, uniform→uniform",
    "stack_half_range is not a hard worst-case bound when +Tol/−Tol are asymmetric about nominal — use stack_worst_plus / stack_worst_minus"
  ],
  "boundary_conditions": [
    "No tol / empty dimensions → MISSING_REQUIRED_INPUT",
    "Bad mode / direction / statistical_basis → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ASME Y14.5 — Dimensioning and Tolerancing",
      "section": "GD&T symbols, rules, and drawing requirements",
      "url": "https://www.asme.org/codes-standards/find-codes-standards/y14-5-dimensioning-tolerancing",
      "supports": "Defines geometric dimensioning and tolerancing language used on engineering drawings; does not itself define the RSS stack-up formula",
      "kind": "standard"
    },
    {
      "title": "Mekid, S. — Metrology and Instrumentation (Wiley-ASME Press)",
      "section": "§6.5.4 Worst-Case Tolerance Stack-Up in Asymmetric Dimensional Tolerance; §6.6.2 Worst-Case vs RSS",
      "url": "https://www.wiley.com/en-us/Metrology+and+Instrumentation%3A+Practical+Applications+for+Engineering+and+Manufacturing-p-9781119721734",
      "supports": "1-D worst-case stack for asymmetric ±tol and comparison of worst-case vs root-sum-square statistical analysis",
      "kind": "reference"
    },
    {
      "title": "SAE 2007-01-0407 — Tolerance Analysis of Mechanical Assemblies with Asymmetric Tolerances",
      "section": "Modified worst-case and RSS accumulation for asymmetric tolerances",
      "url": "https://doi.org/10.4271/2007-01-0407",
      "supports": "Shows that asymmetric contributors produce asymmetric assembly limits; motivates reporting stack_worst_plus / stack_worst_minus separately",
      "kind": "reference"
    },
    {
      "title": "NIST Technical Note 1297",
      "section": "5. Combined standard uncertainty",
      "url": "https://www.nist.gov/pml/nist-technical-note-1297/nist-tn-1297-5-combined-standard-uncertainty",
      "supports": "Root-sum-square combination of independent uncertainty components estimated as standard deviations",
      "kind": "reference"
    },
    {
      "title": "NIST — Evaluating uncertainty components: Type B",
      "section": "Uniform (rectangular) distribution",
      "url": "https://physics.nist.gov/cuu/Uncertainty/typeb.html",
      "supports": "For rectangular limits, best estimate is the interval midpoint (a++a−)/2 and u = a/√3 with a = (a+−a−)/2 — used when statistical_basis=uniform",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:15f47c48aa2f91c65db3252e79e42892fb4b441ca9e5e5c73804cd220335f55b",
  "tests": [
    {
      "id": "rss",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "rss",
        "tol": [
          0.1,
          0.2,
          0.1
        ]
      },
      "expect": {
        "stack": 0.24494897427831783,
        "stack_worst": 0.4
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "basic",
        "n": 3,
        "tol": [
          0.1,
          0.2,
          0.1
        ],
        "stack": 0.24494897427831783,
        "stack_rss": 0.24494897427831783,
        "stack_worst": 0.4,
        "stack_worst_plus": 0.4,
        "stack_worst_minus": 0.4,
        "stack_range": 0.8,
        "stack_half_range": 0.4,
        "stack_nom": null,
        "stack_stat_center": null,
        "stack_center_shift": null,
        "stack_min": null,
        "stack_max": null,
        "rss_over_wca": 0.6123724356957946,
        "dimensions": null
      },
      "tol": 1e-12
    },
    {
      "id": "wca",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "worst_case",
        "tol1": 0.1,
        "tol2": 0.2,
        "tol3": 0.1
      },
      "expect": {
        "stack": 0.4
      },
      "expectWarning": null,
      "actual": {
        "mode": "worst_case",
        "profile": "basic",
        "n": 3,
        "tol": [
          0.1,
          0.2,
          0.1
        ],
        "stack": 0.4,
        "stack_rss": 0.24494897427831783,
        "stack_worst": 0.4,
        "stack_worst_plus": 0.4,
        "stack_worst_minus": 0.4,
        "stack_range": 0.8,
        "stack_half_range": 0.4,
        "stack_nom": null,
        "stack_stat_center": null,
        "stack_center_shift": null,
        "stack_min": null,
        "stack_max": null,
        "rss_over_wca": 0.6123724356957946,
        "dimensions": null
      },
      "tol": 1e-12
    },
    {
      "id": "empty",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss"
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "need at least one tolerance"
    },
    {
      "id": "bad-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "mc",
        "tol1": 0.1
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be \"rss\" or \"worst_case\""
    },
    {
      "id": "tol-alias-tol3",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "rss",
        "tol1": 0.1,
        "tol2": 0.2,
        "tol3": 0.1
      },
      "expect": {
        "stack": 0.24494897427831783,
        "n": 3
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "basic",
        "n": 3,
        "tol": [
          0.1,
          0.2,
          0.1
        ],
        "stack": 0.24494897427831783,
        "stack_rss": 0.24494897427831783,
        "stack_worst": 0.4,
        "stack_worst_plus": 0.4,
        "stack_worst_minus": 0.4,
        "stack_range": 0.8,
        "stack_half_range": 0.4,
        "stack_nom": null,
        "stack_stat_center": null,
        "stack_center_shift": null,
        "stack_min": null,
        "stack_max": null,
        "rss_over_wca": 0.6123724356957946,
        "dimensions": null
      },
      "tol": 1e-12
    },
    {
      "id": "eng-abc",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "rss",
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+"
          },
          {
            "name": "B",
            "nom": 5,
            "tol_plus": 0.2,
            "tol_minus": 0.2,
            "direction": "-"
          },
          {
            "name": "C",
            "nom": 3,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+"
          }
        ]
      },
      "expect": {
        "stack_nom": 8,
        "stack_min": 7.6,
        "stack_max": 8.4,
        "stack_worst": 0.4,
        "stack_rss": 0.24494897427831783
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "engineering",
        "n": 3,
        "tol": [
          0.1,
          0.2,
          0.1
        ],
        "stack": 0.24494897427831783,
        "stack_rss": 0.24494897427831783,
        "stack_worst": 0.4,
        "stack_worst_plus": 0.4,
        "stack_worst_minus": 0.4,
        "stack_range": 0.8,
        "stack_half_range": 0.4,
        "stack_nom": 8,
        "stack_stat_center": 8,
        "stack_center_shift": 0,
        "stack_min": 7.6,
        "stack_max": 8.4,
        "rss_over_wca": 0.6123724356957946,
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": 10,
            "center_shift": 0,
            "signed_center": 10,
            "delta_max": 0.1,
            "delta_min": -0.1,
            "tol_rss": 0.1
          },
          {
            "name": "B",
            "nom": 5,
            "tol_plus": 0.2,
            "tol_minus": 0.2,
            "direction": "-",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": -5,
            "center_shift": 0,
            "signed_center": -5,
            "delta_max": 0.2,
            "delta_min": -0.2,
            "tol_rss": 0.2
          },
          {
            "name": "C",
            "nom": 3,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": 3,
            "center_shift": 0,
            "signed_center": 3,
            "delta_max": 0.1,
            "delta_min": -0.1,
            "tol_rss": 0.1
          }
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-tol8",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
        "tol1": 0.1,
        "tol2": 0.1,
        "tol3": 0.1,
        "tol4": 0.1,
        "tol5": 0.1,
        "tol6": 0.1,
        "tol7": 0.1,
        "tol8": 0.1
      },
      "expect": {
        "n": 8,
        "stack": 0.282842712474619,
        "stack_worst": 0.8
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "basic",
        "n": 8,
        "tol": [
          0.1,
          0.1,
          0.1,
          0.1,
          0.1,
          0.1,
          0.1,
          0.1
        ],
        "stack": 0.28284271247461906,
        "stack_rss": 0.28284271247461906,
        "stack_worst": 0.7999999999999999,
        "stack_worst_plus": 0.7999999999999999,
        "stack_worst_minus": 0.7999999999999999,
        "stack_range": 1.5999999999999999,
        "stack_half_range": 0.7999999999999999,
        "stack_nom": null,
        "stack_stat_center": null,
        "stack_center_shift": null,
        "stack_min": null,
        "stack_max": null,
        "rss_over_wca": 0.35355339059327384,
        "dimensions": null
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-single",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
        "tol1": 0.25
      },
      "expect": {
        "stack": 0.25,
        "stack_worst": 0.25
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "basic",
        "n": 1,
        "tol": [
          0.25
        ],
        "stack": 0.25,
        "stack_rss": 0.25,
        "stack_worst": 0.25,
        "stack_worst_plus": 0.25,
        "stack_worst_minus": 0.25,
        "stack_range": 0.5,
        "stack_half_range": 0.25,
        "stack_nom": null,
        "stack_stat_center": null,
        "stack_center_shift": null,
        "stack_min": null,
        "stack_max": null,
        "rss_over_wca": 1,
        "dimensions": null
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zero-pad",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "worst_case",
        "tol": [
          0.1,
          0,
          0.2
        ]
      },
      "expect": {
        "stack": 0.3,
        "stack_rss": 0.22360679774997896
      },
      "expectWarning": null,
      "actual": {
        "mode": "worst_case",
        "profile": "basic",
        "n": 3,
        "tol": [
          0.1,
          0,
          0.2
        ],
        "stack": 0.30000000000000004,
        "stack_rss": 0.223606797749979,
        "stack_worst": 0.30000000000000004,
        "stack_worst_plus": 0.30000000000000004,
        "stack_worst_minus": 0.30000000000000004,
        "stack_range": 0.6000000000000001,
        "stack_half_range": 0.30000000000000004,
        "stack_nom": null,
        "stack_stat_center": null,
        "stack_center_shift": null,
        "stack_min": null,
        "stack_max": null,
        "rss_over_wca": 0.7453559924999299,
        "dimensions": null
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-invalid-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "montecarlo",
        "tol1": 0.1
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be \"rss\" or \"worst_case\""
    },
    {
      "id": "boundary-eng-abc",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+"
          },
          {
            "name": "B",
            "nom": 5,
            "tol_plus": 0.2,
            "tol_minus": 0.2,
            "direction": "-"
          },
          {
            "name": "C",
            "nom": 3,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+"
          }
        ]
      },
      "expect": {
        "stack_nom": 8,
        "stack_min": 7.6,
        "stack_max": 8.4,
        "stack_worst": 0.4,
        "stack_worst_plus": 0.4,
        "stack_worst_minus": 0.4,
        "stack_half_range": 0.4,
        "stack_rss": 0.2449489742783178
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "engineering",
        "n": 3,
        "tol": [
          0.1,
          0.2,
          0.1
        ],
        "stack": 0.24494897427831783,
        "stack_rss": 0.24494897427831783,
        "stack_worst": 0.4,
        "stack_worst_plus": 0.4,
        "stack_worst_minus": 0.4,
        "stack_range": 0.8,
        "stack_half_range": 0.4,
        "stack_nom": 8,
        "stack_stat_center": 8,
        "stack_center_shift": 0,
        "stack_min": 7.6,
        "stack_max": 8.4,
        "rss_over_wca": 0.6123724356957946,
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": 10,
            "center_shift": 0,
            "signed_center": 10,
            "delta_max": 0.1,
            "delta_min": -0.1,
            "tol_rss": 0.1
          },
          {
            "name": "B",
            "nom": 5,
            "tol_plus": 0.2,
            "tol_minus": 0.2,
            "direction": "-",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": -5,
            "center_shift": 0,
            "signed_center": -5,
            "delta_max": 0.2,
            "delta_min": -0.2,
            "tol_rss": 0.2
          },
          {
            "name": "C",
            "nom": 3,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": 3,
            "center_shift": 0,
            "signed_center": 3,
            "delta_max": 0.1,
            "delta_min": -0.1,
            "tol_rss": 0.1
          }
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-eng-asymm",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "worst_case",
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.05,
            "tol_minus": 0.15,
            "direction": "+"
          },
          {
            "name": "B",
            "nom": 5,
            "tol_plus": 0.2,
            "tol_minus": 0.2,
            "direction": "-"
          },
          {
            "name": "C",
            "nom": 3,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+"
          }
        ]
      },
      "expect": {
        "stack_nom": 8,
        "stack_min": 7.55,
        "stack_max": 8.35,
        "stack_worst_plus": 0.35,
        "stack_worst_minus": 0.45,
        "stack_half_range": 0.4,
        "stack_worst": 0.45,
        "stack_range": 0.8
      },
      "expectWarning": null,
      "actual": {
        "mode": "worst_case",
        "profile": "engineering",
        "n": 3,
        "tol": [
          0.1,
          0.2,
          0.1
        ],
        "stack": 0.44999999999999996,
        "stack_rss": 0.24494897427831783,
        "stack_worst": 0.44999999999999996,
        "stack_worst_plus": 0.35,
        "stack_worst_minus": 0.44999999999999996,
        "stack_range": 0.7999999999999999,
        "stack_half_range": 0.39999999999999997,
        "stack_nom": 8,
        "stack_stat_center": 8,
        "stack_center_shift": 0,
        "stack_min": 7.55,
        "stack_max": 8.35,
        "rss_over_wca": 0.5443310539518175,
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.05,
            "tol_minus": 0.15,
            "direction": "+",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": 10,
            "center_shift": 0,
            "signed_center": 10,
            "delta_max": 0.05,
            "delta_min": -0.15,
            "tol_rss": 0.1
          },
          {
            "name": "B",
            "nom": 5,
            "tol_plus": 0.2,
            "tol_minus": 0.2,
            "direction": "-",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": -5,
            "center_shift": 0,
            "signed_center": -5,
            "delta_max": 0.2,
            "delta_min": -0.2,
            "tol_rss": 0.2
          },
          {
            "name": "C",
            "nom": 3,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+",
            "statistical_basis": "magnitude",
            "distribution": "magnitude",
            "signed_nom": 3,
            "center_shift": 0,
            "signed_center": 3,
            "delta_max": 0.1,
            "delta_min": -0.1,
            "tol_rss": 0.1
          }
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-eng-uniform",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
        "dimensions": [
          {
            "name": "A",
            "nom": 0,
            "tol": 0.3,
            "direction": "+",
            "statistical_basis": "uniform"
          }
        ]
      },
      "expect": {
        "stack_rss": 0.17320508075688773,
        "stack_worst": 0.3,
        "stack_half_range": 0.3
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "engineering",
        "n": 1,
        "tol": [
          0.3
        ],
        "stack": 0.17320508075688773,
        "stack_rss": 0.17320508075688773,
        "stack_worst": 0.3,
        "stack_worst_plus": 0.3,
        "stack_worst_minus": 0.3,
        "stack_range": 0.6,
        "stack_half_range": 0.3,
        "stack_nom": 0,
        "stack_stat_center": 0,
        "stack_center_shift": 0,
        "stack_min": -0.3,
        "stack_max": 0.3,
        "rss_over_wca": 0.5773502691896258,
        "dimensions": [
          {
            "name": "A",
            "nom": 0,
            "tol_plus": 0.3,
            "tol_minus": 0.3,
            "direction": "+",
            "statistical_basis": "uniform",
            "distribution": "uniform",
            "signed_nom": 0,
            "center_shift": 0,
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            "delta_max": 0.3,
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            "tol_rss": 0.17320508075688773
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      "tol": 1e-12
    },
    {
      "id": "boundary-eng-3sigma",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
        "dimensions": [
          {
            "name": "A",
            "nom": 0,
            "tol": 0.3,
            "direction": "+",
            "statistical_basis": "3sigma"
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      "actual": {
        "mode": "rss",
        "profile": "engineering",
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        "tol": [
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        "stack": 0.09999999999999999,
        "stack_rss": 0.09999999999999999,
        "stack_worst": 0.3,
        "stack_worst_plus": 0.3,
        "stack_worst_minus": 0.3,
        "stack_range": 0.6,
        "stack_half_range": 0.3,
        "stack_nom": 0,
        "stack_stat_center": 0,
        "stack_center_shift": 0,
        "stack_min": -0.3,
        "stack_max": 0.3,
        "rss_over_wca": 0.3333333333333333,
        "dimensions": [
          {
            "name": "A",
            "nom": 0,
            "tol_plus": 0.3,
            "tol_minus": 0.3,
            "direction": "+",
            "statistical_basis": "3sigma",
            "distribution": "3sigma",
            "signed_nom": 0,
            "center_shift": 0,
            "signed_center": 0,
            "delta_max": 0.3,
            "delta_min": -0.3,
            "tol_rss": 0.09999999999999999
          }
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-eng-legacy-normal",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
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          {
            "name": "A",
            "nom": 0,
            "tol": 0.3,
            "direction": "+",
            "distribution": "normal"
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      "actual": {
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        "profile": "engineering",
        "n": 1,
        "tol": [
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        ],
        "stack": 0.3,
        "stack_rss": 0.3,
        "stack_worst": 0.3,
        "stack_worst_plus": 0.3,
        "stack_worst_minus": 0.3,
        "stack_range": 0.6,
        "stack_half_range": 0.3,
        "stack_nom": 0,
        "stack_stat_center": 0,
        "stack_center_shift": 0,
        "stack_min": -0.3,
        "stack_max": 0.3,
        "rss_over_wca": 1,
        "dimensions": [
          {
            "name": "A",
            "nom": 0,
            "tol_plus": 0.3,
            "tol_minus": 0.3,
            "direction": "+",
            "statistical_basis": "1sigma",
            "distribution": "1sigma",
            "signed_nom": 0,
            "center_shift": 0,
            "signed_center": 0,
            "delta_max": 0.3,
            "delta_min": -0.3,
            "tol_rss": 0.3
          }
        ]
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      "tol": 1e-12
    },
    {
      "id": "boundary-eng-uniform-center",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.05,
            "tol_minus": 0.15,
            "direction": "+",
            "statistical_basis": "uniform"
          },
          {
            "name": "B",
            "nom": 5,
            "tol": 0.2,
            "direction": "-",
            "statistical_basis": "uniform"
          },
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            "name": "C",
            "nom": 3,
            "tol": 0.1,
            "direction": "+",
            "statistical_basis": "uniform"
          }
        ]
      },
      "expect": {
        "stack_nom": 8,
        "stack_stat_center": 7.95,
        "stack_center_shift": -0.05,
        "stack_min": 7.55,
        "stack_max": 8.35
      },
      "expectWarning": null,
      "actual": {
        "mode": "rss",
        "profile": "engineering",
        "n": 3,
        "tol": [
          0.1,
          0.2,
          0.1
        ],
        "stack": 0.14142135623730953,
        "stack_rss": 0.14142135623730953,
        "stack_worst": 0.44999999999999996,
        "stack_worst_plus": 0.35,
        "stack_worst_minus": 0.44999999999999996,
        "stack_range": 0.7999999999999999,
        "stack_half_range": 0.39999999999999997,
        "stack_nom": 8,
        "stack_stat_center": 7.949999999999999,
        "stack_center_shift": -0.05000000000000071,
        "stack_min": 7.55,
        "stack_max": 8.35,
        "rss_over_wca": 0.31426968052735454,
        "dimensions": [
          {
            "name": "A",
            "nom": 10,
            "tol_plus": 0.05,
            "tol_minus": 0.15,
            "direction": "+",
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            "distribution": "uniform",
            "signed_nom": 10,
            "center_shift": -0.049999999999999996,
            "signed_center": 9.95,
            "delta_max": 0.05,
            "delta_min": -0.15,
            "tol_rss": 0.05773502691896258
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          {
            "name": "B",
            "nom": 5,
            "tol_plus": 0.2,
            "tol_minus": 0.2,
            "direction": "-",
            "statistical_basis": "uniform",
            "distribution": "uniform",
            "signed_nom": -5,
            "center_shift": 0,
            "signed_center": -5,
            "delta_max": 0.2,
            "delta_min": -0.2,
            "tol_rss": 0.11547005383792516
          },
          {
            "name": "C",
            "nom": 3,
            "tol_plus": 0.1,
            "tol_minus": 0.1,
            "direction": "+",
            "statistical_basis": "uniform",
            "distribution": "uniform",
            "signed_nom": 3,
            "center_shift": 0,
            "signed_center": 3,
            "delta_max": 0.1,
            "delta_min": -0.1,
            "tol_rss": 0.05773502691896258
          }
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-eng-empty",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "rss",
        "dimensions": []
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "need at least one tolerance"
    },
    {
      "id": "property-rss",
      "ok": true,
      "kind": "property",
      "detail": "rss",
      "expect": 0.2449489742783178,
      "actual": 0.24494897427831783
    },
    {
      "id": "property-wca",
      "ok": true,
      "kind": "property",
      "detail": "wca",
      "expect": 0.4,
      "actual": 0.4
    },
    {
      "id": "property-permute",
      "ok": true,
      "kind": "property",
      "detail": "order-invariant",
      "expect": 0.24494897427831783,
      "actual": 0.24494897427831783
    },
    {
      "id": "property-zero",
      "ok": true,
      "kind": "property",
      "detail": "zero-pad",
      "expect": 0.24494897427831783,
      "actual": 0.24494897427831783
    },
    {
      "id": "property-single-eq",
      "ok": true,
      "kind": "property",
      "detail": "rss=wca",
      "expect": 0.37,
      "actual": 0.37
    },
    {
      "id": "property-scale",
      "ok": true,
      "kind": "property",
      "detail": "homogeneous",
      "expect": 0.7348469228349535,
      "actual": 0.7348469228349536
    },
    {
      "id": "property-rss-le-wca",
      "ok": true,
      "kind": "property",
      "detail": "rss≤wca",
      "expect": true,
      "actual": true
    },
    {
      "id": "property-tol-alias",
      "ok": true,
      "kind": "property",
      "detail": "tol[]≡tol1…n",
      "expect": 0.24494897427831783,
      "actual": 0.24494897427831783
    },
    {
      "id": "property-eng-nom",
      "ok": true,
      "kind": "property",
      "detail": "nom=8",
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      "actual": 8
    },
    {
      "id": "property-eng-matches-basic",
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      "kind": "property",
      "detail": "eng≡basic-tol",
      "expect": 0.24494897427831783,
      "actual": 0.24494897427831783
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      "id": "property-eng-asymm",
      "ok": true,
      "kind": "property",
      "detail": "asymm-wca",
      "expect": 0.25,
      "actual": 0.25
    },
    {
      "id": "property-eng-asymm-sides",
      "ok": true,
      "kind": "property",
      "detail": "plus/minus",
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      "actual": 0.25
    },
    {
      "id": "property-eng-half-ne-worst",
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      "kind": "property",
      "detail": "half≠worst",
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    },
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      "kind": "property",
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      "actual": "magnitude"
    },
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      "id": "property-eng-uniform-center",
      "ok": true,
      "kind": "property",
      "detail": "uniform-midpoint",
      "expect": 7.95,
      "actual": 7.949999999999999
    },
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      "id": "property-eng-mag-no-shift",
      "ok": true,
      "kind": "property",
      "detail": "mag-center=nom",
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      "actual": 8
    }
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    "tests": {
      "passed": 35,
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      "golden": 4,
      "boundary": 13,
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      "total": 8
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      "items": [
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}