{
  "capability_id": "mechanical.statics.cantilever_moment_deflection",
  "tool_id": "cantilever-moment-deflection",
  "engine": "cantilever-moment-deflection",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-25T01:47:46.268Z",
  "engine_build": "2026-09-24",
  "test_count": 4,
  "passed": 4,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 2,
      "passed": 2
    },
    "boundary": {
      "total": 2,
      "passed": 2
    },
    "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/cantilever-moment-deflection",
  "api": "https://www.calculatorx.com/api/v1/calc/cantilever-moment-deflection",
  "schema_input": "https://www.calculatorx.com/schemas/mechanical.statics.cantilever_moment_deflection.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/mechanical.statics.cantilever_moment_deflection.output.json",
  "assumptions": [],
  "limitations": [
    "Cantilever fixed at one end",
    "One concentrated moment at the free end",
    "I is an input",
    "Not a point load or a uniform load"
  ],
  "boundary_conditions": [
    "missing M, L, E, or I → MISSING_REQUIRED_INPUT",
    "L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE"
  ],
  "sources": [
    {
      "title": "Hibbeler, Mechanics of Materials",
      "section": "Deflection of beams — cantilever with a concentrated moment at the free end",
      "supports": "The free-end deflection is M L² / (2 E I) when the moment sits at the tip of a cantilever.",
      "kind": "reference"
    },
    {
      "title": "Gere and Goodno, Mechanics of Materials",
      "section": "Deflection of beams — cantilever with a concentrated moment at the free end",
      "supports": "Supports the page formula: δ = M L² / (2 E I)",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:36e309babf6a1b8fe9c486db9db23c26f4d61a66a57a129f0f133136cf9584b3",
  "tests": [
    {
      "id": "golden-tip",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "M": 4,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": 8,
        "model": "cantilever_moment_deflection"
      },
      "expectWarning": null,
      "actual": {
        "model": "cantilever_moment_deflection",
        "M": 4,
        "L": 2,
        "E": 1,
        "I": 1,
        "delta": 8,
        "solver": "cantilever end moment",
        "convention": "Cantilever fixed at one end with one concentrated moment at the free end. δ = M L²/(2 E I). Positive M is the positive deflection direction. I is an input. A point load and a uniform load are their own pages."
      },
      "tol": 1e-12
    },
    {
      "id": "golden-sign",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "M": -4,
        "L": 2,
        "E": 1,
        "I": 1
      },
      "expect": {
        "delta": -8
      },
      "expectWarning": null,
      "actual": {
        "model": "cantilever_moment_deflection",
        "M": -4,
        "L": 2,
        "E": 1,
        "I": 1,
        "delta": -8,
        "solver": "cantilever end moment",
        "convention": "Cantilever fixed at one end with one concentrated moment at the free end. δ = M L²/(2 E I). Positive M is the positive deflection direction. I is an input. A point load and a uniform load are their own pages."
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-zero-length",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "M": 4,
        "L": 0,
        "E": 1,
        "I": 1
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "Length L must be positive."
    },
    {
      "id": "boundary-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "M": 4,
        "L": 2,
        "E": 1
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "I is required."
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 4,
      "total": 4,
      "golden": 2,
      "boundary": 2,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-24T12:26:58.772Z",
  "rendered_at": "2026-09-25T01:47:46.268Z",
  "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": "bd3ddf4f5c0789c3d8943ee596a61493a8123e73680881c07cdd5bda5d019d89",
      "output_schema_sha256": "95bc2bf3504f4e02050b6c8e683d9682d5c50d2873a9efc12754c8ad9280607b",
      "evidence_sha256": "b54c4fc85e3248a9802e8fb00a2faa3addf6efb6f95c1d1ba406caef9466a141",
      "evidence_core_sha256": "b54c4fc85e3248a9802e8fb00a2faa3addf6efb6f95c1d1ba406caef9466a141",
      "capability_sha256": "ba7d4c7180c87330cfc783eb1d8740d93c74ab79de7e16763b078a34a74e3438",
      "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"
  }
}
