{
  "capability_id": "mechanical.statics.triangular_load_max_deflection",
  "calculation_version": "1.0.0",
  "protocol_version": "1.0.0-proposed",
  "protocol_document_status": "proposed",
  "verification_revision": "2026-09-27.o2-o3",
  "oracle": {
    "class": "O3",
    "library": "mpmath 1.4.1",
    "mpmath_dps": 80,
    "backend": null,
    "rounding": null,
    "generator_id": "triangular-load-maximum-mpmath-o3",
    "generator_version": "1.0.0",
    "generator_sha256": "65eed1e1b3c54d5a5866b66f765b15c49c1dec3c66c6505b28ac69f88202fc67",
    "table_sha256": "d45d14c2d2706f33abe423b77f5636feb13e52cb3f371ec0a9e930c9770f941a",
    "seed": "20260927.triangular-load-maximum-o3",
    "independent_of_iut": true
  },
  "claim_scope": "O2: delta vs a separate-module identity (≤2 ULP). Not midspan under the same triangle, and not a station curve. ≤2 ULP vs O3 applies only to the published tabulated triangular-load-maximum vectors.",
  "commands": {
    "regenerate_table": "python3 generate-triangular-load-maximum-o3.py",
    "regenerate_table_repo": "python3 scripts/lib/cvp/oracles/generate-triangular-load-maximum-o3.py",
    "independent_rest": "Compare POST /api/v1/calc/triangular-load-maximum against /developers/cvp/reproduce/triangular-load-maximum-o3-tables.json",
    "run_cvp": "npm run cvp:run -- --capability mechanical.statics.triangular_load_max_deflection",
    "rest_example": "POST https://www.calculatorx.com/api/v1/calc/triangular-load-maximum"
  },
  "public_files": {
    "table": "/developers/cvp/reproduce/triangular-load-maximum-o3-tables.json",
    "table_url": "https://www.calculatorx.com/developers/cvp/reproduce/triangular-load-maximum-o3-tables.json",
    "generator": "/developers/cvp/reproduce/generate-triangular-load-maximum-o3.py",
    "generator_url": "https://www.calculatorx.com/developers/cvp/reproduce/generate-triangular-load-maximum-o3.py",
    "checker": "/developers/cvp/reproduce/check-math-o3-rest.py",
    "checker_url": "https://www.calculatorx.com/developers/cvp/reproduce/check-math-o3-rest.py",
    "manifest": "/evidence/mechanical.statics.triangular_load_max_deflection/1.0.0.cvp.json",
    "this_file": "/evidence/mechanical.statics.triangular_load_max_deflection/reproduce.json"
  },
  "result_summary": {
    "passed": 8,
    "total": 8,
    "failed": 0,
    "max_error_ulp": 1,
    "threshold_ulp": 2,
    "max_threshold_ulp": 2
  },
  "vectors": [
    {
      "id": "o3-check",
      "kind": "check",
      "inputs": {
        "w0": "24",
        "L": "2",
        "E": "1",
        "I": "1"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 2.504518745057035,
        "x": 1.0386592447184564,
        "w0": 24,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": 24,
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1.0386592447184564,
        "delta": 2.5045187450570356,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-SI",
      "kind": "SI",
      "inputs": {
        "w0": "1000",
        "L": "2",
        "E": "200000000000",
        "I": "0.00001"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.0000521774738553549,
        "x": 1.0386592447184564,
        "w0": 1000,
        "L": 2,
        "E": 200000000000,
        "I": 0.00001
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": 1000,
        "L": 2,
        "E": 200000000000,
        "I": 0.00001,
        "x": 1.0386592447184564,
        "delta": 0.000052177473855354896,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-alias",
      "kind": "alias",
      "inputs": {
        "w": "48",
        "span": "2",
        "modulus": "1",
        "Ix": "1"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 5.00903749011407,
        "x": 1.0386592447184564,
        "w0": 48,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": 48,
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1.0386592447184564,
        "delta": 5.009037490114071,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-awkward",
      "kind": "awkward",
      "inputs": {
        "w0": "13.7",
        "L": "2",
        "E": "210000",
        "I": "0.83"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.000008202310864238235,
        "x": 1.0386592447184564,
        "w0": 13.7,
        "L": 2,
        "E": 210000,
        "I": 0.83
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": 13.7,
        "L": 2,
        "E": 210000,
        "I": 0.83,
        "x": 1.0386592447184564,
        "delta": 0.000008202310864238235,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-neg",
      "kind": "signed",
      "inputs": {
        "w0": "-24",
        "L": "2",
        "E": "1",
        "I": "1"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": -2.504518745057035,
        "x": 1.0386592447184564,
        "w0": -24,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": -24,
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1.0386592447184564,
        "delta": -2.5045187450570356,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-small",
      "kind": "small",
      "inputs": {
        "w0": "10",
        "L": "2",
        "E": "1000",
        "I": "0.01"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.1043549477107098,
        "x": 1.0386592447184564,
        "w0": 10,
        "L": 2,
        "E": 1000,
        "I": 0.01
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": 10,
        "L": 2,
        "E": 1000,
        "I": 0.01,
        "x": 1.0386592447184564,
        "delta": 0.1043549477107098,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-stiff",
      "kind": "stiff",
      "inputs": {
        "w0": "500",
        "L": "2",
        "E": "210e9",
        "I": "2e-4"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.0000012423208060798786,
        "x": 1.0386592447184564,
        "w0": 500,
        "L": 2,
        "E": 210000000000,
        "I": 0.0002
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": 500,
        "L": 2,
        "E": 210000000000,
        "I": 0.0002,
        "x": 1.0386592447184564,
        "delta": 0.0000012423208060798786,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-long",
      "kind": "long",
      "inputs": {
        "w0": "200",
        "L": "4",
        "E": "70e9",
        "I": "5e-5"
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.00009541023790693468,
        "x": 2.0773184894369128,
        "w0": 200,
        "L": 4,
        "E": 70000000000,
        "I": 0.00005
      },
      "actual": {
        "model": "triangular_load_max_deflection",
        "w0": 200,
        "L": 4,
        "E": 70000000000,
        "I": 0.00005,
        "x": 2.0773184894369128,
        "delta": 0.00009541023790693468,
        "solver": "simply supported triangular load maximum",
        "convention": "Simply supported span. Intensity is 0 at the left support and w0 at the right. The largest deflection is δ = w0 L⁴ √(1−√(8/15)) (2+5√(8/15)) / (450 E I), at x = L √(1−√(8/15)) from the unloaded end. I is an input. The midspan value is its own page."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    }
  ]
}