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  "assumptions": [
    "Trapezoid alternate depths: E = y + Q²/(2g A²) with A=(b+z y)y; both y_sub>yc and y_super<yc at the same E, Q, b, z; SI; default g=9.80665; z>0 is run/rise",
    "Unknown is the pair (depths mode) or E (energy invert from one y); E>Ec=yc+D_c/2; Fr is reported not an input",
    "Not rectangular alternate depth; not trapezoid E from y+Q; not trapezoid yc as the product; not trapezoid yn; not Manning n; not Q=Av"
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    "Trapezoid alternate depths: E = y + Q²/(2g A²) with A=(b+z y)y; both y_sub>yc and y_super<yc at the same E, Q, b, z; SI; default g=9.80665; z>0 is run/rise",
    "Unknown is the pair (depths mode) or E (energy invert from one y); E>Ec=yc+D_c/2; Fr is reported not an input",
    "Not rectangular alternate depth; not trapezoid E from y+Q; not trapezoid yc as the product; not trapezoid yn; not Manning n; not Q=Av"
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    "E ≤ Ec or y/b outside [0.01, 20] or z>10 → VALUE_OUT_OF_RANGE",
    "z=0, A/v, y1/y2, M, Fr/L, n/C/S/R/Sc, yn/yc/q, H/Cd → MIXED_INPUT_ENCODING",
    "unknown mode → INVALID_MODE"
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    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Energy and volume flow",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "E and y are lengths; Q is volume flow",
      "kind": "standard"
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    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Specific energy and alternate depths in a trapezoidal section",
      "supports": "The same E gives two depths when E>Ec. Rectangular both y from E, Q, b is a different product. Trapezoid E from y and Q is a different product.",
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