{
  "capability_id": "mechanical.statics.incline_horizontal",
  "tool_id": "incline-horizontal",
  "engine": "incline-horizontal",
  "calculation_version": "1.0.0",
  "generated_at": "2026-11-10T05:18:42.169Z",
  "engine_build": "2026-09-27",
  "test_count": 7,
  "passed": 7,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 3,
      "total": 3
    },
    "boundary": {
      "passed": 4,
      "total": 4
    },
    "property": {
      "passed": 0,
      "total": 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/mechanical/incline-horizontal",
  "api": "https://www.calculatorx.com/api/v1/calc/incline-horizontal",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.incline_horizontal.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.incline_horizontal.output.json",
  "assumptions": [],
  "limitations": [
    "P is horizontal and positive toward the uphill side",
    "Impending slip, with friction opposing the stated direction",
    "The normal is W cosθ + P sinθ",
    "Not a force parallel to the plane, tipping, a wedge, a screw, or a belt"
  ],
  "boundary_conditions": [
    "missing W, θ, μ, or direction → MISSING_REQUIRED_INPUT",
    "W ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "θ outside [0, 90) or μ < 0 → VALUE_OUT_OF_RANGE",
    "direction other than up or down → INVALID_INPUT"
  ],
  "sources": [
    {
      "title": "Hibbeler, Engineering Mechanics: Statics",
      "section": "Dry friction — a horizontal force on an inclined block",
      "supports": "A horizontal force resolves into P cosθ along the plane and P sinθ into the surface. Impending slip sets the friction magnitude to μN.",
      "kind": "reference"
    },
    {
      "title": "Beer, Johnston, and Mazurek, Vector Mechanics for Engineers: Statics",
      "section": "Dry friction — a horizontal force on an inclined block",
      "supports": "Supports the page formula: N = W cos θ + P sin θ",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:cac70b0cee6b7cc8e940feffecedde673069ed5d50cd1a1c4fab1f800496ff65",
  "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": "2026-09-27T08:15:46.336Z",
  "rendered_at": "2026-11-10T05:18:42.169Z",
  "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": "01093b4048c24c94c5431590c45f3378747b89d9ea8db710e8f242563542e654",
      "output_schema_sha256": "9af856454c720736f03db70393a509877653212320ef543e7adc08269ef30647",
      "evidence_sha256": "f373ab1cfc717a3f82c8d1aff7e23115452d183f6712333fdf6cd19a08183f48",
      "evidence_core_sha256": "f373ab1cfc717a3f82c8d1aff7e23115452d183f6712333fdf6cd19a08183f48",
      "capability_sha256": "a8babc7aa1f2fb400bd17349d3f0d1de502109f7a5b31ce7e6389b0363755783",
      "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"
  }
}