{
  "capability_id": "mechanical.statics.incline_slip_or_tip",
  "tool_id": "incline-slip-or-tip",
  "engine": "incline-slip-or-tip",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-23T14:21:08.538Z",
  "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/incline-slip-or-tip",
  "api": "https://www.calculatorx.com/api/v1/calc/incline-slip-or-tip",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.incline_slip_or_tip.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.incline_slip_or_tip.output.json",
  "assumptions": [],
  "limitations": [
    "The block is a homogeneous rectangle",
    "The only force is its own weight",
    "b is the base along the incline and h is the height perpendicular to it",
    "Not a horizontal force on a level surface, a wedge, a screw, or a belt"
  ],
  "boundary_conditions": [
    "missing μ, b, or h → MISSING_REQUIRED_INPUT",
    "b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "μ < 0 → VALUE_OUT_OF_RANGE"
  ],
  "sources": [
    {
      "title": "Hibbeler, Engineering Mechanics: Statics",
      "section": "Dry friction — tipping or slipping of a block on an incline",
      "supports": "Impending slip down the plane is tanθ = μ. A homogeneous rectangle tips about the downhill edge when tanθ = b/h.",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:39e1e0eadeeb7236b1b70c08a6a0a12361d3af4f406382da91a2fcb7f1bf1603",
  "tests": [
    {
      "id": "golden-either",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mu": 1,
        "b": 2,
        "h": 2
      },
      "expect": {
        "mode": "either",
        "theta_deg": 45,
        "theta_slip_deg": 45,
        "theta_tip_deg": 45,
        "model": "incline_slip_or_tip"
      },
      "expectWarning": null,
      "actual": {
        "model": "incline_slip_or_tip",
        "mu": 1,
        "b": 2,
        "h": 2,
        "mode": "either",
        "theta_deg": 45,
        "theta_slip_deg": 45,
        "theta_tip_deg": 45,
        "solver": "incline friction + moment about the downhill edge",
        "convention": "A homogeneous rectangle rests on the incline under its own weight. b is the base along the incline. h is the height perpendicular to the incline. θslip is the friction angle. θtip is the angle where the vertical through the center passes through the downhill edge, so tanθtip = b/h. The smaller angle happens first as the incline is raised."
      },
      "tol": 1e-9
    },
    {
      "id": "golden-slip",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mu": 0,
        "b": 2,
        "h": 2
      },
      "expect": {
        "mode": "slip",
        "theta_deg": 0,
        "theta_slip_deg": 0,
        "theta_tip_deg": 45
      },
      "expectWarning": null,
      "actual": {
        "model": "incline_slip_or_tip",
        "mu": 0,
        "b": 2,
        "h": 2,
        "mode": "slip",
        "theta_deg": 0,
        "theta_slip_deg": 0,
        "theta_tip_deg": 45,
        "solver": "incline friction + moment about the downhill edge",
        "convention": "A homogeneous rectangle rests on the incline under its own weight. b is the base along the incline. h is the height perpendicular to the incline. θslip is the friction angle. θtip is the angle where the vertical through the center passes through the downhill edge, so tanθtip = b/h. The smaller angle happens first as the incline is raised."
      },
      "tol": 1e-9
    },
    {
      "id": "golden-tip",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mu": 1,
        "b": 1,
        "h": 2
      },
      "expect": {
        "mode": "tip",
        "theta_deg": 26.56505117707799,
        "theta_slip_deg": 45,
        "theta_tip_deg": 26.56505117707799
      },
      "expectWarning": null,
      "actual": {
        "model": "incline_slip_or_tip",
        "mu": 1,
        "b": 1,
        "h": 2,
        "mode": "tip",
        "theta_deg": 26.56505117707799,
        "theta_slip_deg": 45,
        "theta_tip_deg": 26.56505117707799,
        "solver": "incline friction + moment about the downhill edge",
        "convention": "A homogeneous rectangle rests on the incline under its own weight. b is the base along the incline. h is the height perpendicular to the incline. θslip is the friction angle. θtip is the angle where the vertical through the center passes through the downhill edge, so tanθtip = b/h. The smaller angle happens first as the incline is raised."
      },
      "tol": 1e-9
    },
    {
      "id": "boundary-mu",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mu": -0.1,
        "b": 2,
        "h": 2
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "mu must be non-negative."
    },
    {
      "id": "boundary-base",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mu": 1,
        "b": 0,
        "h": 2
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Base b must be positive."
    },
    {
      "id": "boundary-height",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mu": 1,
        "b": 2,
        "h": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Height h must be positive."
    },
    {
      "id": "boundary-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mu": 1,
        "b": 2
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "h 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": "2026-09-23T12:52:44.711Z",
  "rendered_at": "2026-09-23T14:21:08.538Z",
  "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": "014dd65bc33d21b3a7abf8233bebbf36b1e20166412c12eebf508f6ab7e17272",
      "output_schema_sha256": "bd1941a7bd65f2a1b877a2423ac76a3799ef6a08685bb6e693942707e5330aad",
      "evidence_sha256": "16ca17c6d051a103cb7830f6c3713ebca978e11b79cf2b4c7853d59c6b61310f",
      "evidence_core_sha256": "16ca17c6d051a103cb7830f6c3713ebca978e11b79cf2b4c7853d59c6b61310f",
      "capability_sha256": "ef11b1c8421c8dc7ad2e3b86298c86b28d740e58f7724481c1d201e4a8575db0",
      "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"
  }
}