{
  "capability_id": "mechanical.statics.ladder_rough_wall",
  "tool_id": "ladder-rough-wall",
  "engine": "ladder-rough-wall",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-23T14:21:08.537Z",
  "engine_build": "2026-09-23",
  "test_count": 7,
  "passed": 7,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 3,
      "passed": 3
    },
    "boundary": {
      "total": 4,
      "passed": 4
    },
    "property": {
      "total": 0,
      "passed": 0
    }
  },
  "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/ladder-rough-wall",
  "api": "https://www.calculatorx.com/api/v1/calc/ladder-rough-wall",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.ladder_rough_wall.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.ladder_rough_wall.output.json",
  "assumptions": [],
  "limitations": [
    "The ladder is uniform and the weight acts at mid-length",
    "Both surfaces are at impending slip",
    "μwall = 0 is the smooth-wall case",
    "Not a person on the ladder, a wedge, a screw, or a belt"
  ],
  "boundary_conditions": [
    "missing W, μ floor, or μ wall → MISSING_REQUIRED_INPUT",
    "W ≤ 0 or μ floor ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "μ wall < 0 → VALUE_OUT_OF_RANGE"
  ],
  "sources": [
    {
      "title": "Hibbeler, Engineering Mechanics: Statics",
      "section": "Dry friction — ladder with friction at both surfaces",
      "supports": "At impending slip on both surfaces, tanθ = (1 − μ_floor μ_wall) / (2 μ_floor) for a uniform ladder",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:1c2f407bd2ba8b9d8e33d405ecde123c5cbdfedd59f70125423711dd1590434e",
  "tests": [
    {
      "id": "golden-smooth",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "W": 100,
        "mu_floor": 0.5,
        "mu_wall": 0
      },
      "expect": {
        "mode": "angle",
        "theta_deg": 45,
        "N": 100,
        "F": 50,
        "B": 50,
        "F_wall": 0,
        "model": "ladder_rough_wall"
      },
      "expectWarning": null,
      "actual": {
        "model": "ladder_rough_wall",
        "W": 100,
        "mu_floor": 0.5,
        "mu_wall": 0,
        "mode": "angle",
        "theta_deg": 45,
        "N": 100,
        "F": 50,
        "B": 50,
        "F_wall": 0,
        "solver": "friction + math.linear_algebra solve order 2",
        "convention": "Uniform ladder, weight at mid-length. θ is the smallest angle with the floor at which both surfaces are at impending slip. N and F are on the floor. B and F_wall are on the wall, with F_wall upward."
      },
      "tol": 1e-9
    },
    {
      "id": "golden-both",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "W": 100,
        "mu_floor": 0.4,
        "mu_wall": 0.3
      },
      "expect": {
        "mode": "angle",
        "theta_deg": 47.72631099390627,
        "N": 89.28571428571428,
        "F": 35.714285714285715,
        "B": 35.714285714285715,
        "F_wall": 10.714285714285714
      },
      "expectWarning": null,
      "actual": {
        "model": "ladder_rough_wall",
        "W": 100,
        "mu_floor": 0.4,
        "mu_wall": 0.3,
        "mode": "angle",
        "theta_deg": 47.72631099390626,
        "N": 89.2857142857,
        "F": 35.71428571428,
        "B": 35.7142857143,
        "F_wall": 10.714285714289998,
        "solver": "friction + math.linear_algebra solve order 2",
        "convention": "Uniform ladder, weight at mid-length. θ is the smallest angle with the floor at which both surfaces are at impending slip. N and F are on the floor. B and F_wall are on the wall, with F_wall upward."
      },
      "tol": 1e-9
    },
    {
      "id": "golden-any",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "W": 100,
        "mu_floor": 1,
        "mu_wall": 1
      },
      "expect": {
        "mode": "any",
        "theta_deg": null,
        "N": null,
        "F": null,
        "B": null,
        "F_wall": null
      },
      "expectWarning": null,
      "actual": {
        "model": "ladder_rough_wall",
        "W": 100,
        "mu_floor": 1,
        "mu_wall": 1,
        "mode": "any",
        "theta_deg": null,
        "N": null,
        "F": null,
        "B": null,
        "F_wall": null,
        "solver": "friction + math.linear_algebra solve order 2",
        "convention": "Uniform ladder, weight at mid-length. Both surfaces are at impending slip. μfloor·μwall ≥ 1, so the ladder holds at every angle in (0, 90). Reactions are not unique."
      },
      "tol": null
    },
    {
      "id": "boundary-weight",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "W": 0,
        "mu_floor": 0.5,
        "mu_wall": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Weight W must be positive."
    },
    {
      "id": "boundary-floor",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "W": 100,
        "mu_floor": 0,
        "mu_wall": 0.3
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "mu_floor must be positive."
    },
    {
      "id": "boundary-wall",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "W": 100,
        "mu_floor": 0.5,
        "mu_wall": -0.1
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "mu_wall must be non-negative."
    },
    {
      "id": "boundary-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "W": 100,
        "mu_floor": 0.5
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "mu_wall is required."
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 7,
      "total": 7,
      "golden": 3,
      "boundary": 4,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-23T12:25:21.407Z",
  "rendered_at": "2026-09-23T14:21:08.537Z",
  "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": "04ea699edcd3d266d975d539c8f89af314f901a6bfb732b7e83f35b8ccdb9e1c",
      "output_schema_sha256": "73d88426cccf42a70e707412bb3e2f1ce46bdbaa93923828dfb801c169191e5e",
      "evidence_sha256": "d3338f8f40b56980912ea9e192f21fd528939120c0fc2b921b3b219e58f7e64d",
      "evidence_core_sha256": "d3338f8f40b56980912ea9e192f21fd528939120c0fc2b921b3b219e58f7e64d",
      "capability_sha256": "2fee3e0b68566083963457ca33cebbd2053f11a928f4036b6cdbea0a04fd8588",
      "engine_sha256": "208304ca4712067561139ce40e8e989b08ad769a073c83f960c49734a91d8b98",
      "mcp_contract_sha256": "c07b6ccec97dcc960230a1aa48fcea3aad2d3b93ce113ae07c095579f88cbc3b"
    },
    "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"
  }
}