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  "assumptions": [
    "Trapezoid specific force: M = Q²/(gA) + A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; M is m²; z>0 is run/rise",
    "Unknown is M (force mode) or y (depth invert, subcritical y>yc by default); conjugate y_alt is reported; Fr is reported not an input",
    "Not rectangular ȳ=y/2; not trapezoid sequent y2; not trapezoid specific energy E; not Manning n; not Q=Av"
  ],
  "limitations": [
    "Trapezoid specific force: M = Q²/(gA) + A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; M is m²; z>0 is run/rise",
    "Unknown is M (force mode) or y (depth invert, subcritical y>yc by default); conjugate y_alt is reported; Fr is reported not an input",
    "Not rectangular ȳ=y/2; not trapezoid sequent y2; not trapezoid specific energy E; not Manning n; not Q=Av"
  ],
  "boundary_conditions": [
    "missing b, z, Q, y, or M when required → MISSING_REQUIRED_INPUT",
    "y, Q, b, z, M, or g ≤ 0, or y/b outside [0.01, 20], or z>10 → VALUE_OUT_OF_RANGE",
    "z=0, A/v, y1/y2, E, Fr/L, n/C/S/R/Sc, yn/yc/q, H/Cd → MIXED_INPUT_ENCODING",
    "unknown mode → INVALID_MODE"
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  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Volume flow rate and force",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "Q is volume flow; specific force M is force per unit weight (m²)",
      "kind": "standard"
    },
    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Specific force in a trapezoidal section",
      "supports": "M = Q²/(gA) + A ȳ with ȳ from the trapezoid centroid. Rectangular ȳ=y/2 is a different product. Sequent depths are a different product.",
      "kind": "reference"
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  "fingerprint": "sha256:5e32b28c1a508268531b1b85bc260a8e9d8c81a8586b32fde79c536cff172c9b",
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      "ok": true,
      "kind": "property",
      "detail": "M=Q²/(gA)+Aȳ",
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      "detail": "specific_force_trapezoid",
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