{
  "capability_id": "physics.fluid.trapezoid_critical_depth",
  "tool_id": "trapezoidal-critical-depth",
  "engine": "trapezoidal-critical-depth",
  "calculation_version": "1.0.0",
  "generated_at": "2026-11-10T05:18:41.986Z",
  "engine_build": "2026-09-24",
  "test_count": 6,
  "passed": 6,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 1,
      "total": 1
    },
    "boundary": {
      "passed": 0,
      "total": 0
    },
    "property": {
      "passed": 5,
      "total": 5
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/physics/trapezoidal-critical-depth",
  "api": "https://www.calculatorx.com/api/v1/calc/trapezoidal-critical-depth",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_critical_depth.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.trapezoid_critical_depth.output.json",
  "assumptions": [
    "Trapezoid critical depth: Fr=1 with A=(b+z yc) yc and T=b+2 z yc so Q² T = g A³; SI; default g=9.80665; z>0 is run/rise",
    "Critical speed vc = Q/A = √(g A/T) is reported, not an input; Fr=1 is the definition, not a Froude wrap",
    "Not rectangular yc=(q²/g)^{1/3}; not normal-depth yn; not specific energy E; not Manning n; not Q=Av"
  ],
  "limitations": [
    "Trapezoid critical depth: Fr=1 with A=(b+z yc) yc and T=b+2 z yc so Q² T = g A³; SI; default g=9.80665; z>0 is run/rise",
    "Unknown is yc (depth mode) or Q (discharge invert); vc=√(g A/T) is reported; Fr=1 is the definition, not a Froude wrap",
    "Not rectangular yc=(q²/g)^{1/3}; not normal-depth yn; not specific energy E; not Manning n; not Q=Av"
  ],
  "boundary_conditions": [
    "missing Q, b, z, or yc when required → MISSING_REQUIRED_INPUT",
    "Q, b, z, yc, or g ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "z=0, q, n/S/yn, E, Fr/L, A/v, y1/M/Sc, B, theta → MIXED_INPUT_ENCODING",
    "z>10 or yc/b outside [0.01, 20] → VALUE_OUT_OF_RANGE",
    "unit_discharge, energy, or yn as mode → MIXED_INPUT_ENCODING or INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Length, speed, acceleration",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "yc is a length; Q is volume flow; g is acceleration",
      "kind": "standard"
    },
    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Critical flow in a trapezoidal section",
      "supports": "Fr=1 is Q² T = g A³. Rectangular yc=(q²/g)^{1/3} is the z=0 special case on a different page.",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:6f9063673d75fd623c2d489cc3a647d29aaf216de261be304a8caa338cdddf0a",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 6,
      "total": 6,
      "golden": 1,
      "boundary": 0,
      "property": 5
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-24T02:12:38.088Z",
  "rendered_at": "2026-11-10T05:18:41.986Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
      "engine": "1.0.0",
      "page": "1.0.0",
      "capability": "1.0.0",
      "evidence": "1.0.0",
      "input_schema": "1.0.0",
      "output_schema": "1.0.0",
      "mcp_contract": "1.0.0"
    },
    "digests": {
      "input_schema_sha256": "58e996e1feaef67c68521faa5e5cd2d87c403642356cdad1492611db45b3e669",
      "output_schema_sha256": "9ade55c11018764030d6a46206ad886218b0a973645928faf4a28da14fdd967c",
      "evidence_sha256": "97551408f59f35fa788fb54454c8a5c978587eb68c0423cbc96006d6f1e72b35",
      "evidence_core_sha256": "97551408f59f35fa788fb54454c8a5c978587eb68c0423cbc96006d6f1e72b35",
      "capability_sha256": "8fa2d3647f2b09eefbba232396ac04d4d039c6ea2b7add5033c4f002f0b35d75",
      "engine_sha256": "c6ebd8436f08b413e1ac6317b2d48550f2e6639a90dff254244e3aa562158b8d",
      "mcp_contract_sha256": "eb3e39ad4a95ed263415b4932f185d5edfe00a2403267b7c5ed5f718d1ff6da3"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  },
  "tests": [],
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}
