{
  "capability_id": "mechanical.beam.deflection",
  "calculation_version": "1.0.0",
  "protocol_version": "1.0.0-proposed",
  "protocol_document_status": "proposed",
  "verification_revision": "2026-09-27.o2-o3.parent.iface.o3fix",
  "oracle": {
    "class": "O3",
    "library": "mpmath 1.4.1",
    "mpmath_dps": 80,
    "backend": null,
    "rounding": null,
    "generator_id": "beam-deflection-contract-partitioned-o3",
    "generator_version": "1.0.0",
    "generator_sha256": "f84f2547104951ea3db963d2dcdfd8dab72a415796702c4ff180c4882f4be663",
    "table_sha256": "ac85afeb2106dd775e07c517629996243e2a59b8a3f2760d5e262c84a0bd27ac",
    "seed": "20260927.beam-deflection-o3",
    "independent_of_iut": true
  },
  "claim_scope": "O2: delta vs composed Layer-A separate-module identities (≤2 ULP). Multi-load is Σ δ_i. Not FEM, not indeterminate, not generic multi-load max. ≤2 ULP vs O3 applies only to tabulated Layer-A partitions projected from published leaf mpmath tables (simply_supported×point×midspan, cantilever×point×tip, simply_supported×uniform×midspan). Multi-load composition is out of O3 claim scope.",
  "commands": {
    "regenerate_table": "python3 generate-beam-deflection-o3.py",
    "regenerate_table_repo": "python3 scripts/lib/cvp/oracles/generate-beam-deflection-o3.py",
    "independent_rest": "Compare POST /api/v1/calc/mechanical-beam-deflection (contract shape) against partitioned leaf O3 tables under /developers/cvp/reproduce/",
    "run_cvp": "npm run cvp:run -- --capability mechanical.beam.deflection",
    "rest_example": "POST https://www.calculatorx.com/api/v1/calc/mechanical-beam-deflection"
  },
  "public_files": {
    "table": "/developers/cvp/reproduce/beam-deflection-o3-tables.json",
    "table_url": "https://www.calculatorx.com/developers/cvp/reproduce/beam-deflection-o3-tables.json",
    "generator": "/developers/cvp/reproduce/generate-beam-deflection-o3.py",
    "generator_url": "https://www.calculatorx.com/developers/cvp/reproduce/generate-beam-deflection-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.beam.deflection/1.0.0.cvp.json",
    "this_file": "/evidence/mechanical.beam.deflection/reproduce.json"
  },
  "result_summary": {
    "passed": 24,
    "total": 24,
    "failed": 0,
    "max_error_ulp": 1,
    "threshold_ulp": 2,
    "max_threshold_ulp": 2
  },
  "vectors": [
    {
      "id": "ss-point-midspan:o3-check",
      "kind": "check",
      "inputs": {
        "support": "simply_supported",
        "L": 2,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 480
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 80,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 480
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 480,
            "a": null
          }
        ],
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1,
        "delta": 80,
        "components": [
          {
            "id": "P1",
            "delta": 80,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-point-midspan:o3-SI",
      "kind": "SI",
      "inputs": {
        "support": "simply_supported",
        "L": 4,
        "E": 200000000000,
        "I": 0.00001,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 1000
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.0006666666666666665,
        "L": 4,
        "E": 200000000000,
        "I": 0.00001
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 1000
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 1000,
            "a": null
          }
        ],
        "L": 4,
        "E": 200000000000,
        "I": 0.00001,
        "x": 2,
        "delta": 0.0006666666666666665,
        "components": [
          {
            "id": "P1",
            "delta": 0.0006666666666666665,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-point-midspan:o3-alias",
      "kind": "alias",
      "inputs": {
        "support": "simply_supported",
        "L": 2,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 960
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 160,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 960
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 960,
            "a": null
          }
        ],
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1,
        "delta": 160,
        "components": [
          {
            "id": "P1",
            "delta": 160,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-point-midspan:o3-awkward",
      "kind": "awkward",
      "inputs": {
        "support": "simply_supported",
        "L": 3.5,
        "E": 210000,
        "I": 0.83,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 137
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.0007020791499330656,
        "L": 3.5,
        "E": 210000,
        "I": 0.83
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 137
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 137,
            "a": null
          }
        ],
        "L": 3.5,
        "E": 210000,
        "I": 0.83,
        "x": 1.75,
        "delta": 0.0007020791499330656,
        "components": [
          {
            "id": "P1",
            "delta": 0.0007020791499330656,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-point-midspan:o3-neg",
      "kind": "signed",
      "inputs": {
        "support": "simply_supported",
        "L": 2,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": -480
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": -80,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": -480
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": -480,
            "a": null
          }
        ],
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 1,
        "delta": -80,
        "components": [
          {
            "id": "P1",
            "delta": -80,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-point-midspan:o3-small",
      "kind": "small",
      "inputs": {
        "support": "simply_supported",
        "L": 1,
        "E": 1000,
        "I": 0.01,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 10
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.020833333333333332,
        "L": 1,
        "E": 1000,
        "I": 0.01
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 10
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 10,
            "a": null
          }
        ],
        "L": 1,
        "E": 1000,
        "I": 0.01,
        "x": 0.5,
        "delta": 0.020833333333333332,
        "components": [
          {
            "id": "P1",
            "delta": 0.020833333333333332,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-point-midspan:o3-stiff",
      "kind": "stiff",
      "inputs": {
        "support": "simply_supported",
        "L": 3,
        "E": 210000000000,
        "I": 0.0002,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 5000
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.00006696428571428572,
        "L": 3,
        "E": 210000000000,
        "I": 0.0002
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 5000
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 5000,
            "a": null
          }
        ],
        "L": 3,
        "E": 210000000000,
        "I": 0.0002,
        "x": 1.5,
        "delta": 0.00006696428571428572,
        "components": [
          {
            "id": "P1",
            "delta": 0.00006696428571428572,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-point-midspan:o3-long",
      "kind": "long",
      "inputs": {
        "support": "simply_supported",
        "L": 8,
        "E": 70000000000,
        "I": 0.00005,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 200
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.0006095238095238095,
        "L": 8,
        "E": 70000000000,
        "I": 0.00005
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 200
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 200,
            "a": null
          }
        ],
        "L": 8,
        "E": 70000000000,
        "I": 0.00005,
        "x": 4,
        "delta": 0.0006095238095238095,
        "components": [
          {
            "id": "P1",
            "delta": 0.0006095238095238095,
            "model": "offset_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-check",
      "kind": "check",
      "inputs": {
        "support": "cantilever",
        "L": 2,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 3
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 8,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 3
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 3,
            "a": null
          }
        ],
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 2,
        "delta": 8,
        "components": [
          {
            "id": "P1",
            "delta": 8,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-SI",
      "kind": "SI",
      "inputs": {
        "support": "cantilever",
        "L": 2,
        "E": 200000000000,
        "I": 0.00001,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 1000
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.001333333333333333,
        "L": 2,
        "E": 200000000000,
        "I": 0.00001
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 1000
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 1000,
            "a": null
          }
        ],
        "L": 2,
        "E": 200000000000,
        "I": 0.00001,
        "x": 2,
        "delta": 0.001333333333333333,
        "components": [
          {
            "id": "P1",
            "delta": 0.001333333333333333,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-alias",
      "kind": "alias",
      "inputs": {
        "support": "cantilever",
        "L": 2,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 6
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 16,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 6
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 6,
            "a": null
          }
        ],
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 2,
        "delta": 16,
        "components": [
          {
            "id": "P1",
            "delta": 16,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-awkward",
      "kind": "awkward",
      "inputs": {
        "support": "cantilever",
        "L": 3.5,
        "E": 210000,
        "I": 0.83,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 13.7
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.001123326639892905,
        "L": 3.5,
        "E": 210000,
        "I": 0.83
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 13.7
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 13.7,
            "a": null
          }
        ],
        "L": 3.5,
        "E": 210000,
        "I": 0.83,
        "x": 3.5,
        "delta": 0.0011233266398929047,
        "components": [
          {
            "id": "P1",
            "delta": 0.0011233266398929047,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-neg",
      "kind": "signed",
      "inputs": {
        "support": "cantilever",
        "L": 2,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": -3
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": -8,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": -3
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": -3,
            "a": null
          }
        ],
        "L": 2,
        "E": 1,
        "I": 1,
        "x": 2,
        "delta": -8,
        "components": [
          {
            "id": "P1",
            "delta": -8,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-small",
      "kind": "small",
      "inputs": {
        "support": "cantilever",
        "L": 1,
        "E": 1000,
        "I": 0.01,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 10
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.3333333333333333,
        "L": 1,
        "E": 1000,
        "I": 0.01
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 10
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 10,
            "a": null
          }
        ],
        "L": 1,
        "E": 1000,
        "I": 0.01,
        "x": 1,
        "delta": 0.3333333333333333,
        "components": [
          {
            "id": "P1",
            "delta": 0.3333333333333333,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-stiff",
      "kind": "stiff",
      "inputs": {
        "support": "cantilever",
        "L": 1.5,
        "E": 210000000000,
        "I": 0.0002,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 500
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.000013392857142857142,
        "L": 1.5,
        "E": 210000000000,
        "I": 0.0002
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 500
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 500,
            "a": null
          }
        ],
        "L": 1.5,
        "E": 210000000000,
        "I": 0.0002,
        "x": 1.5,
        "delta": 0.000013392857142857142,
        "components": [
          {
            "id": "P1",
            "delta": 0.000013392857142857142,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "cantilever-point-tip:o3-long",
      "kind": "long",
      "inputs": {
        "support": "cantilever",
        "L": 4,
        "E": 70000000000,
        "I": 0.00005,
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 200
          }
        ],
        "query": {
          "kind": "tip"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.001219047619047619,
        "L": 4,
        "E": 70000000000,
        "I": 0.00005
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "cantilever",
        "query": {
          "kind": "tip"
        },
        "loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 200
          }
        ],
        "normalized_loads": [
          {
            "id": "P1",
            "type": "point",
            "P": 200,
            "a": null
          }
        ],
        "L": 4,
        "E": 70000000000,
        "I": 0.00005,
        "x": 4,
        "delta": 0.001219047619047619,
        "components": [
          {
            "id": "P1",
            "delta": 0.001219047619047619,
            "model": "cantilever_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-check",
      "kind": "check",
      "inputs": {
        "support": "simply_supported",
        "L": 1,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 384
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 5,
        "L": 1,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 384
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 384
          }
        ],
        "L": 1,
        "E": 1,
        "I": 1,
        "x": 0.5,
        "delta": 5,
        "components": [
          {
            "id": "U1",
            "delta": 5,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-SI",
      "kind": "SI",
      "inputs": {
        "support": "simply_supported",
        "L": 2,
        "E": 200000000000,
        "I": 0.00001,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 1000
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.00010416666666666665,
        "L": 2,
        "E": 200000000000,
        "I": 0.00001
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 1000
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 1000
          }
        ],
        "L": 2,
        "E": 200000000000,
        "I": 0.00001,
        "x": 1,
        "delta": 0.00010416666666666665,
        "components": [
          {
            "id": "U1",
            "delta": 0.00010416666666666665,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-alias",
      "kind": "alias",
      "inputs": {
        "support": "simply_supported",
        "L": 1,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 768
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 10,
        "L": 1,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 768
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 768
          }
        ],
        "L": 1,
        "E": 1,
        "I": 1,
        "x": 0.5,
        "delta": 10,
        "components": [
          {
            "id": "U1",
            "delta": 10,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-awkward",
      "kind": "awkward",
      "inputs": {
        "support": "simply_supported",
        "L": 3.5,
        "E": 210000,
        "I": 0.83,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 13.7
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.0001535798140478581,
        "L": 3.5,
        "E": 210000,
        "I": 0.83
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 13.7
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 13.7
          }
        ],
        "L": 3.5,
        "E": 210000,
        "I": 0.83,
        "x": 1.75,
        "delta": 0.00015357981404785808,
        "components": [
          {
            "id": "U1",
            "delta": 0.00015357981404785808,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-neg",
      "kind": "signed",
      "inputs": {
        "support": "simply_supported",
        "L": 1,
        "E": 1,
        "I": 1,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": -384
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": -5,
        "L": 1,
        "E": 1,
        "I": 1
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": -384
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": -384
          }
        ],
        "L": 1,
        "E": 1,
        "I": 1,
        "x": 0.5,
        "delta": -5,
        "components": [
          {
            "id": "U1",
            "delta": -5,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-small",
      "kind": "small",
      "inputs": {
        "support": "simply_supported",
        "L": 1,
        "E": 1000,
        "I": 0.01,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 10
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.013020833333333334,
        "L": 1,
        "E": 1000,
        "I": 0.01
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 10
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 10
          }
        ],
        "L": 1,
        "E": 1000,
        "I": 0.01,
        "x": 0.5,
        "delta": 0.013020833333333334,
        "components": [
          {
            "id": "U1",
            "delta": 0.013020833333333334,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-stiff",
      "kind": "stiff",
      "inputs": {
        "support": "simply_supported",
        "L": 1.5,
        "E": 210000000000,
        "I": 0.0002,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 500
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 7.847377232142857e-7,
        "L": 1.5,
        "E": 210000000000,
        "I": 0.0002
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 500
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 500
          }
        ],
        "L": 1.5,
        "E": 210000000000,
        "I": 0.0002,
        "x": 0.75,
        "delta": 7.847377232142857e-7,
        "components": [
          {
            "id": "U1",
            "delta": 7.847377232142857e-7,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "ss-uniform-midspan:o3-long",
      "kind": "long",
      "inputs": {
        "support": "simply_supported",
        "L": 4,
        "E": 70000000000,
        "I": 0.00005,
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 200
          }
        ],
        "query": {
          "kind": "midspan"
        }
      },
      "expected_f64": {
        "oracle_layer": "analytic",
        "delta": 0.00019047619047619048,
        "L": 4,
        "E": 70000000000,
        "I": 0.00005
      },
      "actual": {
        "model": "mechanical.beam.deflection",
        "support": "simply_supported",
        "query": {
          "kind": "midspan"
        },
        "loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 200
          }
        ],
        "normalized_loads": [
          {
            "id": "U1",
            "type": "uniform",
            "w": 200
          }
        ],
        "L": 4,
        "E": 70000000000,
        "I": 0.00005,
        "x": 2,
        "delta": 0.00019047619047619048,
        "components": [
          {
            "id": "U1",
            "delta": 0.00019047619047619048,
            "model": "uniform_load_at_deflection"
          }
        ],
        "solver": "beam.deflection superposition of Layer-A At-curves",
        "convention": "Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."
      },
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    }
  ]
}