{
  "capability_id": "math.arcsin",
  "tool_id": "arcsin",
  "engine": "arcsin",
  "calculation_version": "1.0.5",
  "generated_at": "2026-09-16T22:03:43.779Z",
  "engine_build": "2026-09-10",
  "test_count": 11,
  "passed": 11,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 6,
      "passed": 6
    },
    "boundary": {
      "total": 5,
      "passed": 5
    },
    "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/math/arcsin",
  "api": "https://www.calculatorx.com/api/v1/calc/arcsin",
  "schema_input": "https://www.calculatorx.com/schemas/math.arcsin.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.arcsin.output.json",
  "assumptions": [
    "Real inverse sine with principal branch [−π/2, π/2] (NIST DLMF §4.23(ii)). Complex arcsin is not returned.",
    "Opposite/hypotenuse in the UI is a local triangle convenience (hypotenuse > 0, opposite ≥ 0, opposite ≤ hypotenuse). The published engine is arcsin(x). Use Decimal for a signed ratio, and Sin for the forward map.",
    "When x is exactly a listed common value (0, ±1/2, ±√2/2, ±√3/2, ±1), the engine returns the exact algebraic angle such as 30° = π/6. Nearby floats are not snapped."
  ],
  "limitations": [
    "x outside [−1, 1] → NOT_REAL",
    "Missing x → MISSING_REQUIRED_INPUT"
  ],
  "boundary_conditions": [
    "Missing x returns MISSING_REQUIRED_INPUT.",
    "Non-numeric, object, array, boolean, NaN, or Infinity inputs return INVALID_NUMBER.",
    "x < −1 or x > 1 returns NOT_REAL (not clamped).",
    "arcsin(−1) = −90°; arcsin(0) = 0°; arcsin(0.5) = 30°; arcsin(1) = 90°."
  ],
  "sources": [
    {
      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "section": "Elementary Functions",
      "url": "https://dlmf.nist.gov/4",
      "supports": "Inverse trigonometric functions as elementary inverses of sine, cosine, and tangent",
      "kind": "reference"
    },
    {
      "title": "NIST DLMF §4.23",
      "section": "Inverse trigonometric functions; principal values",
      "url": "https://dlmf.nist.gov/4.23",
      "supports": "Principal arcsin on [−1, 1] with range [−π/2, π/2]; degree output is θ × 180/π",
      "kind": "reference"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Principal branch; exact-value recognition; triangle mode is UI-only",
      "supports": "Published engine is arcsin(x). Opposite/hypotenuse is a local triangle convenience (positive sides, opposite ≤ hypotenuse). Inputs outside [−1, 1] are NOT_REAL.",
      "kind": "definition"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:4953573189c37b0f083d599a9bb748776f1bccdfcf9ad01a1848131122926ea0",
  "tests": [
    {
      "id": "half",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "x": 0.5
      },
      "expect": {
        "deg": 30,
        "rad": 0.5235987755982988
      },
      "expectWarning": null,
      "actual": {
        "deg": 30,
        "rad": 0.5235987755982988,
        "verification": {
          "expression": "sin(result)",
          "value": 0.49999999999999994,
          "passed": true
        },
        "exact": true
      },
      "tol": 1e-12
    },
    {
      "id": "one",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "x": 1
      },
      "expect": {
        "deg": 90
      },
      "expectWarning": null,
      "actual": {
        "deg": 90,
        "rad": 1.5707963267948966,
        "verification": {
          "expression": "sin(result)",
          "value": 1,
          "passed": true
        },
        "exact": true
      },
      "tol": 0
    },
    {
      "id": "zero",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "x": 0
      },
      "expect": {
        "deg": 0,
        "rad": 0
      },
      "expectWarning": null,
      "actual": {
        "deg": 0,
        "rad": 0,
        "verification": {
          "expression": "sin(result)",
          "value": 0,
          "passed": true
        },
        "exact": true
      },
      "tol": 0
    },
    {
      "id": "neg",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "x": -1
      },
      "expect": {
        "deg": -90
      },
      "expectWarning": null,
      "actual": {
        "deg": -90,
        "rad": -1.5707963267948966,
        "verification": {
          "expression": "sin(result)",
          "value": -1,
          "passed": true
        },
        "exact": true
      },
      "tol": 0
    },
    {
      "id": "sqrt2-over-2",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "x": 0.7071067811865476
      },
      "expect": {
        "deg": 45
      },
      "expectWarning": null,
      "actual": {
        "deg": 45,
        "rad": 0.7853981633974483,
        "verification": {
          "expression": "sin(result)",
          "value": 0.7071067811865475,
          "passed": true
        },
        "exact": true
      },
      "tol": 0
    },
    {
      "id": "out-of-domain",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "x": 2
      },
      "expectError": "NOT_REAL",
      "code": "NOT_REAL",
      "error": "Real inverse sine/cosine requires x in [−1, 1]."
    },
    {
      "id": "neg-out-of-domain",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "x": -1.1
      },
      "expectError": "NOT_REAL",
      "code": "NOT_REAL",
      "error": "Real inverse sine/cosine requires x in [−1, 1]."
    },
    {
      "id": "missing-x",
      "ok": true,
      "kind": "boundary",
      "inputs": {},
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "Enter a finite value x."
    },
    {
      "id": "x-abc",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "x": "abc"
      },
      "expectError": "INVALID_NUMBER",
      "code": "INVALID_NUMBER",
      "error": "Enter a finite number."
    },
    {
      "id": "x-object",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "x": {}
      },
      "expectError": "INVALID_NUMBER",
      "code": "INVALID_NUMBER",
      "error": "Enter a finite number."
    },
    {
      "id": "oddness",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "x": -0.5
      },
      "expect": {
        "deg": -30
      },
      "expectWarning": null,
      "actual": {
        "deg": -30,
        "rad": -0.5235987755982988,
        "verification": {
          "expression": "sin(result)",
          "value": -0.49999999999999994,
          "passed": true
        },
        "exact": true
      },
      "tol": 0
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 11,
      "total": 11,
      "golden": 6,
      "boundary": 5,
      "property": 0
    },
    "contract_checks": {
      "passed": 3,
      "total": 3
    }
  },
  "evidence_core_generated_at": "2026-09-10T22:48:17.762Z",
  "rendered_at": "2026-09-16T22:03:43.779Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.5",
    "artifacts": {
      "engine": "1.0.5",
      "page": "1.0.5",
      "capability": "1.0.5",
      "evidence": "1.0.5",
      "input_schema": "1.0.5",
      "output_schema": "1.0.5",
      "mcp_contract": "1.0.5"
    },
    "digests": {
      "input_schema_sha256": "641160f19a9efb5244e923b248dfcb154664532e49d7513a9c76395b68579fa5",
      "output_schema_sha256": "a4feb150689f71cbdce87fc4184f3fb38209adf430ce4fe41b93d7cdd4ed69d0",
      "evidence_sha256": "ea4f0280e1d3a7d427ffef911813d4f98dfcf95a31e4f1bacb1f6746e58cd1f9",
      "evidence_core_sha256": "ea4f0280e1d3a7d427ffef911813d4f98dfcf95a31e4f1bacb1f6746e58cd1f9",
      "capability_sha256": "48a96ee49d2dcc6479136ef593aacff7a811cf31cfc0c7b57678f8bcbd7ec5de",
      "engine_sha256": "c8d4ccdbfeaf61d7b024d4e1babb0c2ba3b324c1b37bd0cb456a526d8d2b1bd1",
      "mcp_contract_sha256": "863098b311a7b17dc4b229a6302b90b3545b175f716e5d84772c7be8e9716b86"
    },
    "contract_checks": {
      "total": 3,
      "passed": 3,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.5"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}