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  "internally_reviewed": false,
  "review_kind": null,
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  "reviewer_role": null,
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      "assumptions",
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      "sources",
      "tests"
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  "assumptions": [
    "Froude Fr = v / √(g L); default g=9.80665 m/s²",
    "Free-surface: Fr<1 subcritical, Fr=1 critical, Fr>1 supercritical",
    "Not Reynolds, not Manning, not Chezy, not Q=Av"
  ],
  "limitations": [
    "Froude Fr = v / √(g L); default g=9.80665 m/s²",
    "Free-surface: Fr<1 subcritical, Fr=1 critical, Fr>1 supercritical",
    "Not Reynolds, not Manning, not Chezy, not Q=Av"
  ],
  "boundary_conditions": [
    "missing v, L, or Fr when required → MISSING_REQUIRED_INPUT",
    "v, L, Fr, or g ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "Re/ρ/μ/ν, n, C/R/S, A/Q → MIXED_INPUT_ENCODING",
    "reynolds, manning, or chezy as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-11 — Characteristic numbers",
      "section": "Froude number Fr",
      "supports": "Fr = v / √(l g); gravity/inertia, not viscous Reynolds",
      "kind": "standard"
    },
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Velocity, length, acceleration",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "v has dimension length/time; L length; g acceleration",
      "kind": "standard"
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      "ok": true,
      "kind": "golden",
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        "L": 1
      },
      "expect": {
        "Fr": 0.31932995678105874,
        "v": 1,
        "L": 1,
        "g": 9.80665,
        "regime": "subcritical",
        "mode": "Fr",
        "model": "froude"
      },
      "expectWarning": null,
      "actual": {
        "mode": "Fr",
        "Fr": 0.31932995678105874,
        "v": 1,
        "L": 1,
        "g": 9.80665,
        "regime": "subcritical",
        "model": "froude"
      },
      "tol": 1e-12
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    {
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      "ok": true,
      "kind": "golden",
      "inputs": {
        "v": 3.1315571206669692,
        "L": 1
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      "expect": {
        "Fr": 1,
        "regime": "critical",
        "model": "froude"
      },
      "expectWarning": null,
      "actual": {
        "mode": "Fr",
        "Fr": 1,
        "v": 3.1315571206669692,
        "L": 1,
        "g": 9.80665,
        "regime": "critical",
        "model": "froude"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-fr-v",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "velocity",
        "Fr": 1,
        "L": 1
      },
      "expect": {
        "v": 3.1315571206669692,
        "model": "froude"
      },
      "expectWarning": null,
      "actual": {
        "mode": "velocity",
        "Fr": 1,
        "v": 3.1315571206669692,
        "L": 1,
        "g": 9.80665,
        "regime": "critical",
        "model": "froude"
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      "tol": 1e-12
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    {
      "id": "boundary-fr-L",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "length",
        "Fr": 1,
        "v": 3.1315571206669692
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      "expect": {
        "L": 1,
        "model": "froude"
      },
      "expectWarning": null,
      "actual": {
        "mode": "length",
        "Fr": 1,
        "v": 3.1315571206669692,
        "L": 1,
        "g": 9.80665,
        "regime": "critical",
        "model": "froude"
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-fr-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "L": 1
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "v is required"
    },
    {
      "id": "boundary-fr-v0",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v": 0,
        "L": 1
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "v must be greater than zero"
    },
    {
      "id": "boundary-fr-Re",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v": 1,
        "L": 1,
        "Re": 200000
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Froude does not take Reynolds Re, ρ, μ, or ν. That is /calc/physics/reynolds"
    },
    {
      "id": "boundary-fr-rho",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v": 1,
        "L": 1,
        "rho": 1000
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Froude does not take Reynolds Re, ρ, μ, or ν. That is /calc/physics/reynolds"
    },
    {
      "id": "boundary-fr-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v": 1,
        "L": 1,
        "n": 0.013
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Froude does not take Manning n or Chezy C/R/S. That is /calc/physics/manning-formula or /calc/physics/chezy-formula"
    },
    {
      "id": "boundary-fr-A",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v": 1,
        "L": 1,
        "A": 1
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Froude does not take Q=Av A/Q. That is /calc/physics/flow-rate"
    },
    {
      "id": "boundary-fr-reynolds",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v": 1,
        "L": 1,
        "mode": "reynolds"
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be Fr|velocity|length. Not Reynolds, Manning, Chezy, or Q=Av"
    },
    {
      "id": "boundary-fr-C",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v": 1,
        "L": 1,
        "C": 50
      },
      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Froude does not take Manning n or Chezy C/R/S. That is /calc/physics/manning-formula or /calc/physics/chezy-formula"
    },
    {
      "id": "property-fr-value",
      "ok": true,
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      "detail": "Fr=v/√(gL)",
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      "actual": 0.31932995678105874
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      "id": "property-fr-g-default",
      "ok": true,
      "kind": "property",
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      "expect": 9.80665,
      "actual": 9.80665
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      "ok": true,
      "kind": "property",
      "detail": "Fr=1",
      "expect": 1,
      "actual": 1
    },
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      "ok": true,
      "kind": "property",
      "detail": "v invert",
      "expect": 1,
      "actual": 1
    },
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      "id": "property-fr-model",
      "ok": true,
      "kind": "property",
      "detail": "froude",
      "expect": true,
      "actual": "froude"
    }
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