{
  "capability_id": "mechanical.statics.end_end_moments_at_deflection",
  "tool_id": "end-end-moments-at",
  "engine": "end-end-moments-at",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-25T01:47:46.290Z",
  "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/end-end-moments-at",
  "api": "https://www.calculatorx.com/api/v1/calc/end-end-moments-at",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.end_end_moments_at_deflection.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.end_end_moments_at_deflection.output.json",
  "assumptions": [],
  "limitations": [
    "Peaks at the supports",
    "Equal sagging end moments",
    "I is an input"
  ],
  "boundary_conditions": [
    "missing w0, M, x, L, E, or I → MISSING_REQUIRED_INPUT",
    "L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "x ≤ 0 or x ≥ L → INVALID_INPUT"
  ],
  "sources": [
    {
      "title": "Hibbeler, Mechanics of Materials",
      "section": "Deflection of beams — superposition",
      "supports": "An end-peaked triangle and equal end moments superpose.",
      "kind": "reference"
    },
    {
      "title": "Gere and Goodno, Mechanics of Materials",
      "section": "Deflection of beams — distributed load and end moments",
      "supports": "Supports adding the elastic curves of the two actions.",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:e5d3e2c804bb7f445d6d4c1b91c8c03f8f454196e12565561118e5bebf3aeefb",
  "tests": [
    {
      "id": "golden-mid",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "w0": 24,
        "M": 16,
        "x": 1,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": 9.8,
        "model": "end_end_moments_at_deflection"
      },
      "expectWarning": null,
      "actual": {
        "model": "end_end_moments_at_deflection",
        "w0": 24,
        "M": 16,
        "x": 1,
        "L": 2,
        "E": 1,
        "I": 1,
        "delta": 9.8,
        "solver": "end-peaked triangle plus equal end moments at a station",
        "convention": "Simply supported span with a triangle peaking at both supports and equal sagging end moments M. Deflection at x is the sum of those two curves. x = L/2 is the sum of the two midspan pages."
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-support",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "w0": 24,
        "M": 16,
        "x": 2,
        "L": 2,
        "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": "2026-09-25T00:15:20.818Z",
  "rendered_at": "2026-09-25T01:47:46.290Z",
  "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": "fe803c3ce75fa1bbab062ad1fe2a475c5e0b485362e80d1ce2b530fa47284276",
      "output_schema_sha256": "ad6fecdd8bfeb40596c0fea7fffff2cad6203e0d44cc627164fc95d9e0ec846a",
      "evidence_sha256": "2048083fd1f32a8ce7add0deb487a89527800719949841d47570e8d0f91079ef",
      "evidence_core_sha256": "2048083fd1f32a8ce7add0deb487a89527800719949841d47570e8d0f91079ef",
      "capability_sha256": "b224a3692df4e2c1d59ae7e24b382664dceae28b7edd193391dd7c659a89f99a",
      "engine_sha256": "08114baefe55904e75ed849baa2ac95371b8b8133c19b39348ee1070175d5f3e",
      "mcp_contract_sha256": "9cf7d41527923e8ab8bfc3047f2db08da2aa448cbb98c0359c1d2dfd503a1c40"
    },
    "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"
  }
}