{
  "capability_id": "math.exponent",
  "calculation_version": "1.0.4",
  "protocol_version": "1.0.0-proposed",
  "protocol_document_status": "proposed",
  "verification_revision": "2026-09-08.xcal",
  "oracle": {
    "class": "O3",
    "library": "mpmath 1.4.1",
    "mpmath_dps": 80,
    "backend": "python",
    "rounding": "round-to-nearest-binary64",
    "generator_id": "math-mpmath-o3",
    "generator_version": "1.0.0",
    "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
    "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
    "seed": "20260907",
    "independent_of_iut": true
  },
  "claim_scope": "≤2 ULP vs O3 applies to the 6 published tabulated vectors ((2,10), (10,2), (5,0), (9,0.5), (2,−3), (e,1)). It is not a guarantee over all real bases and exponents.",
  "commands": {
    "regenerate_table": "python3 generate-math-o3.py",
    "regenerate_table_repo": "python3 scripts/lib/cvp/oracles/generate-math-o3.py",
    "independent_rest": "python3 check-math-o3-rest.py exponent",
    "run_cvp": "npm run cvp:run -- --capability math.exponent",
    "rest_example": "POST https://www.calculatorx.com/api/v1/calc/exponent"
  },
  "public_files": {
    "table": "/developers/cvp/reproduce/math-o3-tables.json",
    "table_url": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
    "generator": "/developers/cvp/reproduce/generate-math-o3.py",
    "generator_url": "https://www.calculatorx.com/developers/cvp/reproduce/generate-math-o3.py",
    "checker": "/developers/cvp/reproduce/check-math-o3-rest.py",
    "checker_url": "https://www.calculatorx.com/developers/cvp/reproduce/check-math-o3-rest.py",
    "manifest": "/evidence/math.exponent/1.0.4.cvp.json",
    "this_file": "/evidence/math.exponent/reproduce.json"
  },
  "result_summary": {
    "passed": 6,
    "total": 6,
    "failed": 0,
    "max_error_ulp": 0,
    "threshold_ulp": 2,
    "max_threshold_ulp": 2
  },
  "vectors": [
    {
      "id": "o3-exp-2-10",
      "kind": "interior",
      "inputs": {
        "a": 2,
        "n": 10
      },
      "expected_f64": 1024,
      "expected_decimal": "1024.000000000000000000000000000000000000",
      "actual": 1024,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-exp-10-2",
      "kind": "interior",
      "inputs": {
        "a": 10,
        "n": 2
      },
      "expected_f64": 100,
      "expected_decimal": "100.0000000000000000000000000000000000000",
      "actual": 100,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-exp-5-0",
      "kind": "interior",
      "inputs": {
        "a": 5,
        "n": 0
      },
      "expected_f64": 1,
      "expected_decimal": "1.000000000000000000000000000000000000000",
      "actual": 1,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-exp-9-0.5",
      "kind": "interior",
      "inputs": {
        "a": 9,
        "n": 0.5
      },
      "expected_f64": 3,
      "expected_decimal": "3.000000000000000000000000000000000000000",
      "actual": 3,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-exp-2--3",
      "kind": "interior",
      "inputs": {
        "a": 2,
        "n": -3
      },
      "expected_f64": 0.125,
      "expected_decimal": "0.1250000000000000000000000000000000000000",
      "actual": 0.125,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-exp-2.718281828459045-1",
      "kind": "interior",
      "inputs": {
        "a": 2.718281828459045,
        "n": 1
      },
      "expected_f64": 2.718281828459045,
      "expected_decimal": "2.718281828459045235360287471352662497757",
      "actual": 2.718281828459045,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    }
  ]
}