{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "arctan",
    "version": "1.0.7",
    "title": "Arctangent Calculator",
    "formula_family": "arctan",
    "capability_id": "math.arctan"
  },
  "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": "arctan",
    "version": "1.0.7",
    "uri": "https://www.calculatorx.com/evidence/math.arctan/1.0.7.json"
  },
  "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-DIM-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": "Elementary Functions",
        "url": "https://dlmf.nist.gov/4"
      },
      {
        "label": "NIST DLMF §4.23",
        "kind": "other",
        "reference": "Inverse trigonometric functions; principal values",
        "url": "https://dlmf.nist.gov/4.23"
      },
      {
        "label": "CalculatorX mathematical conventions",
        "kind": "other",
        "reference": "Principal branch; exact-value recognition; ratio mode is UI-only"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Principal inverse tangent (NIST DLMF §4.23)"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath 1.4.1 atan (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*",
        "engine": {
          "name": "atan-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 deg; ≤2 ULP on tabulated vectors only, not the whole domain. Distinct from legacy Evidence case-level tol.",
        "engine": {
          "name": "atan-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 arctan oracle — independent Math.atan + snap",
        "engine": {
          "name": "arctan-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤2 ULP deg comparison vs IUT",
        "engine": {
          "name": "arctan-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      }
    ],
    "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node Math.atan). O2 is a live oracle for identities and shares V8 binary64 with the IUT."
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "principal arctan(x) on (−π/2, π/2)"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "any finite real x; mathematical principal range (−90°, 90°); binary64 may round to ±90°"
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "dimensionless x → angle out (deg and rad)"
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O3 expected_values/numerical_behavior (mpmath table) + O2 live identities"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "7/7 legacy golden; 9/9 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3 invalid-domain cases"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "CVP ≤2 ULP vs O3 when tabulated; legacy Evidence `tol` is not this policy"
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 declared partitions (arctan, invalid-domain, xcal) · 7 golden / 3 boundary unique cases · 3 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 arctan; 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 1.0.7 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.7 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20"
    },
    "CVP-DIM-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "dimensionless x → angle (deg/rad)"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "8/8 property"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "3/3 metamorphic"
    },
    "CVP-ROUND-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "4/4 round-trips"
    },
    "CVP-XCAL-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "4/4 cross-calculator · xcal-tan-one PASS vs math.tan; xcal-tan-zero PASS vs math.tan; xcal-tan-neg-one PASS vs math.tan; xcal-tan-quarter PASS vs math.tan; xcal-tan-huge-na N/A (tan(arctan(x))=x is not a binary64 identity when arctan saturates to ±90° (e.g. x=1e20). Those endpoints are covered by property tests, not XCAL.); xcal-arcsin-na N/A (Arcsin is listed as a related inverse-trig tool. It does not encode tan(arctan(x))=x; domain is [−1,1] with a different inverse.); xcal-arccos-na N/A (Arccos is listed as a related inverse-trig tool. It does not encode tan(arctan(x))=x.); xcal-sin-na N/A (Sin is listed as a related forward-trig tool. It does not encode tan(arctan(x))=x.)"
    },
    "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 21/21 tabulated vectors vs IUT"
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "expert_reviewed=false"
    }
  },
  "tests": {
    "golden": {
      "passed": 9,
      "total": 9,
      "failed": 0,
      "case_ids": [
        "g-atan-1",
        "g-atan-zero",
        "g-atan-neg-one",
        "g-atan-no-snap",
        "g-atan-ten",
        "g-atan-tiny",
        "g-atan-1e10",
        "g-atan-1e20",
        "g-atan-max"
      ]
    },
    "boundary": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "missing-x",
        "x-abc",
        "x-infinity"
      ]
    },
    "invalid": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "missing-x",
        "x-abc",
        "x-infinity"
      ]
    },
    "property": {
      "passed": 8,
      "total": 8,
      "failed": 0,
      "case_ids": [
        "prop-range-one",
        "prop-range-zero",
        "prop-range-ten",
        "prop-range-1e10",
        "prop-binary64-1e20",
        "prop-binary64-max",
        "prop-no-flush-tiny",
        "prop-increasing"
      ],
      "definition_ids": [
        "principal-range",
        "binary64-endpoint-rounding",
        "canonical-no-display-flush",
        "strictly-increasing"
      ]
    },
    "round_trip": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "rt-one",
        "rt-zero",
        "rt-neg-one",
        "rt-quarter"
      ]
    },
    "metamorphic": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "meta-odd-one",
        "meta-odd-ten",
        "meta-odd-quarter"
      ],
      "definition_ids": [
        "arctan-odd"
      ]
    },
    "contract": {
      "passed": 1,
      "total": 1,
      "failed": 0
    },
    "cross_interface": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "iface-atan"
      ]
    },
    "cross_calculator": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "xcal-tan-one",
        "xcal-tan-zero",
        "xcal-tan-neg-one",
        "xcal-tan-quarter"
      ]
    },
    "ui_integration": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "ui-atan-one",
        "ui-atan-no-snap",
        "ui-atan-neg-one",
        "ui-atan-outside-overview"
      ]
    },
    "o3": {
      "passed": 21,
      "total": 21,
      "failed": 0,
      "case_ids": [
        "o3-atan-zero",
        "o3-atan-one",
        "o3-atan-neg-one",
        "o3-atan-sqrt3",
        "o3-atan-inv-sqrt3",
        "o3-atan-no-snap",
        "o3-atan-ten",
        "o3-atan-neg-ten",
        "o3-atan-quarter",
        "o3-atan-tiny",
        "o3-atan-1e10",
        "o3-atan-1e20",
        "o3-atan-max",
        "o3-atan-rand-00",
        "o3-atan-rand-01",
        "o3-atan-rand-02",
        "o3-atan-rand-03",
        "o3-atan-rand-04",
        "o3-atan-rand-05",
        "o3-atan-rand-06",
        "o3-atan-rand-07"
      ],
      "generator_id": "math-mpmath-o3",
      "seed": "20260907",
      "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
      "max_error_ulp": 1,
      "reproduce": "python3 generate-math-o3.py"
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "arctan",
        "description": "arctan(x)",
        "exercised": true,
        "case_count": 56
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 3
      },
      {
        "id": "xcal",
        "description": "Cross-calculator tan(arctan(x))≈x vs published Tan; other related tools N/A",
        "exercised": true,
        "case_count": 4
      }
    ]
  },
  "numerical": {
    "representation": "IEEE-754 binary64 Math.atan with textbook snap; no display-style flush of tiny deg/rad",
    "tolerance": {
      "type": "ulp",
      "value": 2,
      "rationale": "Independent atan + snap vs IUT; ≤2 ULP on deg. Canonical values are not display-flushed. Declared a priori.",
      "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.",
    "max_error_observed": 1,
    "records": [
      {
        "id": "g-atan-1",
        "reference": 45,
        "actual": 45,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-zero",
        "reference": 0,
        "actual": 0,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-neg-one",
        "reference": -45,
        "actual": -45,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-no-snap",
        "reference": 45.0000000257831,
        "actual": 45.0000000257831,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-ten",
        "reference": 84.28940686250036,
        "actual": 84.28940686250037,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-tiny",
        "reference": 5.729577951308232e-19,
        "actual": 5.729577951308233e-19,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-1e10",
        "reference": 89.99999999427042,
        "actual": 89.99999999427042,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-1e20",
        "reference": 90,
        "actual": 90,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-atan-max",
        "reference": 90,
        "actual": 90,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-zero",
        "reference": 0,
        "actual": 0,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-one",
        "reference": 45,
        "actual": 45,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-neg-one",
        "reference": -45,
        "actual": -45,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-sqrt3",
        "reference": 60,
        "actual": 60,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-inv-sqrt3",
        "reference": 30.000000000000004,
        "actual": 30,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-no-snap",
        "reference": 45.0000000257831,
        "actual": 45.0000000257831,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-ten",
        "reference": 84.28940686250036,
        "actual": 84.28940686250037,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-neg-ten",
        "reference": -84.28940686250036,
        "actual": -84.28940686250037,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-quarter",
        "reference": 14.036243467926479,
        "actual": 14.036243467926477,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-tiny",
        "reference": 5.729577951308232e-19,
        "actual": 5.729577951308233e-19,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-1e10",
        "reference": 89.99999999427042,
        "actual": 89.99999999427042,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-1e20",
        "reference": 90,
        "actual": 90,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-max",
        "reference": 90,
        "actual": 90,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-00",
        "reference": -6.839277462411052,
        "actual": -6.839277462411053,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-01",
        "reference": -33.65582720337377,
        "actual": -33.65582720337377,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-02",
        "reference": 21.792370563187152,
        "actual": 21.792370563187152,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-03",
        "reference": 26.751106710317057,
        "actual": 26.75110671031706,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-04",
        "reference": 5.794688885349835,
        "actual": 5.794688885349836,
        "error_ulp": 1,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-05",
        "reference": -2.876936974021086,
        "actual": -2.876936974021086,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-06",
        "reference": -4.789076217162255,
        "actual": -4.789076217162255,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-atan-rand-07",
        "reference": -4.892502244611383,
        "actual": -4.892502244611383,
        "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": "ce3eb452c0c3cedeb49dc2fa152fad5654380907c03050f499069c836f54c585",
    "evidence_digest": "cf317536e8dd9dfcbd1d400e305b97fd335d742afd545e16f3141b246b79466a",
    "production_sha256": "9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20",
    "attested_catalog_sha256": "e03ef81b30568018b171fd1fc4757c2abe9df7220d9ff35bbaf08038d7630cdb",
    "production_checks": [
      {
        "id": "math.arctan:output-const",
        "status": "pass",
        "detail": "output const 1.0.7 vs capability 1.0.7",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.arctan:evidence-sha256",
        "status": "pass",
        "detail": "3976529b8653",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.arctan:semantic-contract",
        "status": "pass",
        "detail": "10/10",
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}