{
  "capability_id": "mechanical.statics.offset_uniform_end_moments_at_deflection",
  "tool_id": "offset-uniform-end-moments-at",
  "engine": "offset-uniform-end-moments-at",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-25T11:22:03.125Z",
  "engine_build": "2026-09-25",
  "test_count": 2,
  "passed": 2,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 1,
      "passed": 1
    },
    "boundary": {
      "total": 1,
      "passed": 1
    },
    "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/offset-uniform-end-moments-at",
  "api": "https://www.calculatorx.com/api/v1/calc/offset-uniform-end-moments-at",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.offset_uniform_end_moments_at_deflection.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.offset_uniform_end_moments_at_deflection.output.json",
  "assumptions": [],
  "limitations": [
    "I is an input"
  ],
  "boundary_conditions": [
    "missing w, P, M, a, x, L, E, or I → MISSING_REQUIRED_INPUT",
    "L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "a ≤ 0, a ≥ L, x ≤ 0, or x ≥ L → INVALID_INPUT"
  ],
  "sources": [
    {
      "title": "Hibbeler, Mechanics of Materials",
      "section": "Deflection of beams — superposition",
      "supports": "A uniform load, a point load, and end moments superpose.",
      "kind": "reference"
    },
    {
      "title": "Gere and Goodno, Mechanics of Materials",
      "section": "Deflection of beams — superposition",
      "supports": "Supports adding the elastic curves of the three actions.",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:98f3b0f646d8231a1161d65f938ec5fc0b1d1610cbd64512ffe675e80b3e431e",
  "tests": [
    {
      "id": "golden-at-load",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "w": 24,
        "P": 48,
        "M": 16,
        "a": 1,
        "x": 1,
        "L": 4,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": 117,
        "model": "offset_uniform_end_moments_at_deflection"
      },
      "expectWarning": null,
      "actual": {
        "model": "offset_uniform_end_moments_at_deflection",
        "w": 24,
        "P": 48,
        "M": 16,
        "a": 1,
        "x": 1,
        "L": 4,
        "E": 1,
        "I": 1,
        "delta": 117,
        "solver": "offset load plus uniform load plus equal end moments at a station",
        "convention": "Simply supported span with an offset load P, a uniform load w, and equal sagging end moments M. Deflection at x is the sum of those curves. x = a is the sum of the offset-uniform page and the end-moments page."
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-support",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "w": 24,
        "P": 48,
        "M": 16,
        "a": 1,
        "x": 0,
        "L": 4,
        "E": 1,
        "I": 1
      },
      "expectError": "INVALID_INPUT",
      "code": "INVALID_INPUT",
      "error": "Station x must lie strictly between the supports."
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 2,
      "total": 2,
      "golden": 1,
      "boundary": 1,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-25T10:56:15.438Z",
  "rendered_at": "2026-09-25T11:22:03.125Z",
  "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": "c8204af0f32043ba2e324363d07af11eca930a5123783bf7b777a8507d1e0a6f",
      "output_schema_sha256": "52fc0bf9d6e357cb4834d46511d98e3b51c306b7fc12c0f1697d5e150f2e55d1",
      "evidence_sha256": "dae5f2a48c7da23031b8e839726b0d946960dbe0d5694d97bda6f2123df59c8c",
      "evidence_core_sha256": "dae5f2a48c7da23031b8e839726b0d946960dbe0d5694d97bda6f2123df59c8c",
      "capability_sha256": "983a4820d69b164e9025811ca6e5b187af2d00cbc7ebfb6012963c79c5d432fd",
      "engine_sha256": "f4f8ea36daaf2ebe1d361158f3aabb71aadcb2fd13c604151ddd8107eb9e8686",
      "mcp_contract_sha256": "c870a2f4e63d79deaea3036d226b61185d7326d98c047ee1cc1475cc8efb6e9c"
    },
    "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"
  }
}