{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "exponent",
    "version": "1.0.4",
    "title": "Exponent Calculator",
    "formula_family": "exponentiation",
    "capability_id": "math.exponent",
    "verification_revision": "2026-09-08.xcal"
  },
  "profile": "core",
  "status": "VERIFIED",
  "runner": {
    "name": "cvp-runner",
    "version": "1.0.0"
  },
  "environment": {
    "runtime": "node",
    "runtime_version": "20.19.2",
    "numeric_model": "IEEE-754 binary64",
    "os": "darwin"
  },
  "suite": {
    "id": "exponent",
    "version": "1.0.4",
    "uri": "https://www.calculatorx.com/evidence/math.exponent/1.0.4.json",
    "verification_revision": "2026-09-08.xcal"
  },
  "obligation_set": [
    "CVP-PROV-01",
    "CVP-MODEL-01",
    "CVP-SCOPE-01",
    "CVP-UNIT-01",
    "CVP-REF-01",
    "CVP-GOLD-01",
    "CVP-BND-01",
    "CVP-INV-01",
    "CVP-NUM-01",
    "CVP-COV-01",
    "CVP-CONTRACT-01",
    "CVP-DEP-01",
    "CVP-ART-01",
    "CVP-PROD-01",
    "CVP-PROP-01",
    "CVP-META-01",
    "CVP-ROUND-01",
    "CVP-XCAL-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "NIST Digital Library of Mathematical Functions, Chapter 4",
        "kind": "other",
        "reference": "Logarithm, Exponential, Powers",
        "url": "https://dlmf.nist.gov/4"
      },
      {
        "label": "NIST DLMF §4.2",
        "kind": "other",
        "reference": "Logarithm and the exponential as inverse operations",
        "url": "https://dlmf.nist.gov/4.2"
      },
      {
        "label": "CalculatorX mathematical conventions",
        "kind": "other",
        "reference": "0^0 undefined; negative base only with integer exponent"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Real exponentiation a^n"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath 1.4.1 exponent (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*",
        "engine": {
          "name": "exponent-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "rounding": "round-to-nearest-binary64",
          "backend": "python",
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
          "seed": "20260907",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/math-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-math-o3.py",
          "public_checker": "/developers/cvp/reproduce/check-math-o3-rest.py"
        }
      },
      {
        "class": "O3",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O3 table vs IUT value; ≤2 ULP on tabulated vectors only, not the whole domain. Distinct from legacy Evidence case-level tol.",
        "engine": {
          "name": "exponent-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "rounding": "round-to-nearest-binary64",
          "backend": "python",
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
          "seed": "20260907",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/math-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-math-o3.py",
          "public_checker": "/developers/cvp/reproduce/check-math-o3-rest.py"
        }
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module exponent oracle — independent a^n",
        "engine": {
          "name": "exponent-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤2 ULP comparison vs IUT",
        "engine": {
          "name": "exponent-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      }
    ],
    "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node ** / Math.exp). O2 is a live oracle for identities and shares V8 binary64 with the IUT. O3 ≤2 ULP is a tabulated-vector claim, not a whole-domain guarantee."
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "y = a^n (forward golden)"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Real forward power; inverse via solve_for"
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "dimensionless (unitless core)"
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O3 mpmath a^n table + O2 live identities"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "16/16 legacy golden; 3/3 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "22/22 boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "21 invalid-domain cases"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "≤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. Legacy Evidence `tol` is not this policy."
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "5/5 declared partitions (forward, solve-base, solve-exp, invalid-domain, xcal) · 16 golden / 22 boundary unique cases · 21 Evidence invalid-input (may overlap boundary)"
    },
    "CVP-CONTRACT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "1/1 contract checks"
    },
    "CVP-DEP-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "engine exponent; Node binary64"
    },
    "CVP-ART-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "release_integrity.status=verified · evidence_digest=CVP verification fingerprint v2 (canonical inputs, expected/actual/status, policy, versions; independent of generated_at) · evidence_bundle_sha256=legacy Evidence JSON bytes · production_sha256=bound production attestation report"
    },
    "CVP-PROD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "CURRENT · site report pass · local checks pass · attestation_id=00c818a77ba026c2d6aa3f7402680cd2dac2a40a816209600bc3c3fcd0b8921c · CURRENT · Public schema 1.0.4 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.4 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-reproduce-manifest-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20"
    },
    "CVP-DIM-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "Unitless core calculator — no physical dimension algebra"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "2/2 property"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "2/2 metamorphic"
    },
    "CVP-ROUND-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "3/3 round-trips"
    },
    "CVP-XCAL-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "11/11 cross-calculator · xcal-root-2-10 PASS vs math.root; xcal-root-10-2 PASS vs math.root; xcal-root-2-3 PASS vs math.root; xcal-log-n0 PASS vs math.log; xcal-log-n1 PASS vs math.log; xcal-log-n2 PASS vs math.log; xcal-antilog-n0 PASS vs math.antilog; xcal-antilog-n1 PASS vs math.antilog; xcal-antilog-n2 PASS vs math.antilog; xcal-sqrt-half PASS vs math.square_root; xcal-sqrt-square PASS vs math.square_root"
    },
    "CVP-IFACE-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session."
    },
    "CVP-ORACLE-01": {
      "result": "PASS",
      "applicability": "higher_assurance",
      "notes": "O3 6/6 tabulated vectors vs IUT · ≤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."
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "expert_reviewed=false"
    }
  },
  "tests": {
    "golden": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "g-2-10",
        "g-10-2",
        "g-5-0"
      ]
    },
    "boundary": {
      "passed": 22,
      "total": 22,
      "failed": 0,
      "case_ids": [
        "zero-to-zero",
        "zero-neg",
        "neg-sqrt",
        "overflow",
        "underflow",
        "empty-a",
        "empty-n",
        "empty-both",
        "a-object",
        "n-array",
        "n-boolean",
        "a-infinity",
        "n-nan",
        "a-abc",
        "solve-base-even-two-reals",
        "solve-base-even-neg",
        "solve-base-n-zero-y-one",
        "solve-base-n-zero-y-two",
        "solve-exp-one-one",
        "solve-exp-one-two",
        "solve-exp-zero-zero",
        "invalid-solve-for"
      ]
    },
    "invalid": {
      "passed": 21,
      "total": 21,
      "failed": 0,
      "case_ids": [
        "zero-to-zero",
        "zero-neg",
        "neg-sqrt",
        "overflow",
        "underflow",
        "empty-a",
        "empty-n",
        "empty-both",
        "a-object",
        "n-array",
        "n-boolean",
        "a-infinity",
        "n-nan",
        "a-abc",
        "solve-base-even-neg",
        "solve-base-n-zero-y-one",
        "solve-base-n-zero-y-two",
        "solve-exp-one-one",
        "solve-exp-one-two",
        "solve-exp-zero-zero",
        "invalid-solve-for"
      ]
    },
    "property": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "prop-a-0",
        "prop-a-1"
      ],
      "definition_ids": [
        "a-to-zero",
        "a-to-one"
      ]
    },
    "round_trip": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "rt-2-10",
        "rt-10-2",
        "rt-log-100"
      ]
    },
    "metamorphic": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "meta-add-exp",
        "meta-add-exp-10"
      ],
      "definition_ids": [
        "a-m-plus-n"
      ]
    },
    "contract": {
      "passed": 1,
      "total": 1,
      "failed": 0
    },
    "cross_interface": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "iface-exp"
      ]
    },
    "cross_calculator": {
      "passed": 11,
      "total": 11,
      "failed": 0,
      "case_ids": [
        "xcal-root-2-10",
        "xcal-root-10-2",
        "xcal-root-2-3",
        "xcal-log-n0",
        "xcal-log-n1",
        "xcal-log-n2",
        "xcal-antilog-n0",
        "xcal-antilog-n1",
        "xcal-antilog-n2",
        "xcal-sqrt-half",
        "xcal-sqrt-square"
      ]
    },
    "ui_integration": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "ui-exp-2-1",
        "ui-exp-5-0",
        "ui-exp-2-2",
        "ui-exp-2-10"
      ]
    },
    "o3": {
      "passed": 6,
      "total": 6,
      "failed": 0,
      "case_ids": [
        "o3-exp-2-10",
        "o3-exp-10-2",
        "o3-exp-5-0",
        "o3-exp-9-0.5",
        "o3-exp-2--3",
        "o3-exp-2.718281828459045-1"
      ],
      "generator_id": "math-mpmath-o3",
      "seed": "20260907",
      "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
      "max_error_ulp": 0,
      "reproduce": "python3 generate-math-o3.py",
      "table_url": "/developers/cvp/reproduce/math-o3-tables.json",
      "generator_url": "/developers/cvp/reproduce/generate-math-o3.py",
      "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.",
      "reproduce_url": "https://www.calculatorx.com/evidence/math.exponent/reproduce"
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "forward",
        "description": "Forward y = a^n",
        "exercised": true,
        "case_count": 40
      },
      {
        "id": "solve-base",
        "description": "Solve base a",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "solve-exp",
        "description": "Solve exponent n",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 21
      },
      {
        "id": "xcal",
        "description": "Cross-calculator ⁿ√(aⁿ)=a vs Root, log₁₀(10ⁿ)=n vs Log, 10ⁿ=antilog(n,10) vs Antilog, √(a²)=|a| / a^(1/2)=√a vs Square root",
        "exercised": true,
        "case_count": 11
      }
    ]
  },
  "numerical": {
    "representation": "IEEE-754 binary64 a**n / Math.exp",
    "tolerance": {
      "type": "ulp",
      "value": 2,
      "rationale": "Independent a^n vs IUT exponent; ≤2 ULP on tabulated O3 vectors, declared a priori. Not a whole-domain ULP guarantee.",
      "declared_before_evaluation": true
    },
    "legacy_regression_notes": "Legacy Evidence JSON may record case-level tol (e.g. 1e-8). That is a regression epsilon, not the CVP ≤2 ULP acceptance policy. CVP records list reference, actual, error_ulp, and the a-priori ULP threshold.",
    "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.",
    "max_error_observed": 0,
    "records": [
      {
        "id": "g-2-10",
        "reference": 1024,
        "actual": 1024,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-10-2",
        "reference": 100,
        "actual": 100,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-5-0",
        "reference": 1,
        "actual": 1,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-exp-2-10",
        "reference": 1024,
        "actual": 1024,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-exp-10-2",
        "reference": 100,
        "actual": 100,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-exp-5-0",
        "reference": 1,
        "actual": 1,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-exp-9-0.5",
        "reference": 3,
        "actual": 3,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-exp-2--3",
        "reference": 0.125,
        "actual": 0.125,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-exp-2.718281828459045-1",
        "reference": 2.718281828459045,
        "actual": 2.718281828459045,
        "error_ulp": 0,
        "threshold_ulp": 2
      }
    ]
  },
  "interfaces": {
    "compared": [
      "ui-ssr",
      "rest",
      "mcp",
      "ui-url-result-graph"
    ],
    "result": "PASS",
    "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session."
  },
  "artifacts": {
    "evidence_bundle_sha256": "75f403d22f33da1bebfbb4e0b5b21a6b14708188d029d0e361bebb0319d7b24b",
    "evidence_digest": "e5bdc1674386f1b25faf08a12ebed7e947862cc02ab3cba50f34de53b23ca1bf",
    "production_sha256": "9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20",
    "attested_catalog_sha256": "e03ef81b30568018b171fd1fc4757c2abe9df7220d9ff35bbaf08038d7630cdb",
    "production_checks": [
      {
        "id": "math.exponent:output-const",
        "status": "pass",
        "detail": "output const 1.0.4 vs capability 1.0.4",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponent:evidence-sha256",
        "status": "pass",
        "detail": "78594fd6780c",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponent:semantic-contract",
        "status": "pass",
        "detail": "38/38",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponent:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.4 vs origin 1.0.4",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponent:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.exponent/1.0.4/2026-09-08.xcal/core/e5bdc1674386",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z",
        "projection_compared": false,
        "observed_live_projection_at_attestation": "VERIFIED"
      },
      {
        "id": "math.exponent:cvp-reproduce-manifest-agree",
        "status": "pass",
        "detail": "2026-09-08.xcal · efdad939a92a",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponent:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Manifest",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponent:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Manifest",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      }
    ]
  },
  "dependencies": [
    {
      "name": "exponent-engine",
      "version": "1.0.4"
    },
    {
      "name": "exponent-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "exponent-o3-mpmath-table",
      "version": "math-mpmath-o3"
    },
    {
      "name": "math.root",
      "version": "1.0.5",
      "role": "cross_calculator_peer",
      "capability_id": "math.root",
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