{
  "capability_id": "physics.fluid.critical_slope",
  "tool_id": "critical-slope",
  "engine": "critical-slope",
  "calculation_version": "1.0.0",
  "generated_at": "2026-11-10T05:18:41.983Z",
  "engine_build": "2026-09-24",
  "test_count": 7,
  "passed": 7,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 1,
      "total": 1
    },
    "boundary": {
      "passed": 0,
      "total": 0
    },
    "property": {
      "passed": 6,
      "total": 6
    }
  },
  "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/critical-slope",
  "api": "https://www.calculatorx.com/api/v1/calc/critical-slope",
  "schema_input": "https://www.calculatorx.com/schemas/physics.fluid.critical_slope.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/physics.fluid.critical_slope.output.json",
  "assumptions": [
    "Rectangular yn=yc: Sc=[n Q/(A R^{2/3})]^2 at yc=(q²/g)^{1/3}; A=b yc; R=b yc/(b+2 yc); SI k=1; Sc is unknown in slope mode",
    "yc/b∈[0.2, 10]; n∈[0.008, 0.15]; Sc∈[1e-6, 0.1]; geometry is b, not A and R; default g=9.80665",
    "Not Manning Q with given A,R,S; not normal-depth yn invert; not critical-depth yc as the product; not Chezy C; not Q=Av; not trapezoid z"
  ],
  "limitations": [
    "Rectangular critical slope: Sc such that yn=yc; SI Manning at y=yc; yc=(q²/g)^{1/3}; Sc=[n Q/(A R^{2/3})]^2 with A=b yc, R=b yc/(b+2 yc)",
    "yc/b∈[0.2, 10] so Sc(yc) is one-to-one; n∈[0.008, 0.15]; Sc∈[1e-6, 0.1]; SI k=1; default g=9.80665",
    "Not Manning Q from A,R,S; not normal-depth yn invert; not critical-depth yc as the product; not Chezy C; not Q=Av; not US k=1.486; not trapezoid z"
  ],
  "boundary_conditions": [
    "missing b, n, Q, or Sc when required → MISSING_REQUIRED_INPUT",
    "yc/b, n, or Sc outside envelope → VALUE_OUT_OF_RANGE",
    "A/R, yn, yc/q, S, E, Chezy C, v, B, z, y1, H, Fr → MIXED_INPUT_ENCODING",
    "unknown mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Volume flow rate and hydraulic radius",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "Q is volume flow; hydraulic radius R = A/P",
      "kind": "standard"
    },
    {
      "title": "Chow, V.T. Open-Channel Hydraulics",
      "section": "Critical slope and critical depth",
      "supports": "Sc is the bed slope at which uniform yn equals critical yc. Not Manning with given A,R as a product page, not yc as the unknown, not Chezy C",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:bc9a288576771706814724bcd8a2b1fac2ac806f56efcf6eef1b5c6303a20fc4",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 7,
      "total": 7,
      "golden": 1,
      "boundary": 0,
      "property": 6
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-24T02:12:38.088Z",
  "rendered_at": "2026-11-10T05:18:41.983Z",
  "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": "bee92c1340983c10f27f9c26074189b5114bd975d4239a68133acbf4cd8a6e54",
      "output_schema_sha256": "36cce11023a310bc4ca0d3e3bba85cad8e58b9e240728139dd5d9e60000b873a",
      "evidence_sha256": "c2689aa6c980bdf20b5f692709fcc5f3af61a693a8c824e5ae722b60717545fe",
      "evidence_core_sha256": "c2689aa6c980bdf20b5f692709fcc5f3af61a693a8c824e5ae722b60717545fe",
      "capability_sha256": "5d65525e628c9135eb2b4d71b6f577262a558e23c50dd86d15dce8ba115f3c60",
      "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"
  }
}
