{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "cos",
    "version": "1.0.5",
    "title": "Cosine Calculator",
    "formula_family": "cosine",
    "capability_id": "math.cos",
    "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": "cos",
    "version": "1.0.5",
    "uri": "https://www.calculatorx.com/evidence/math.cos/1.0.5.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-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 §4.14",
        "kind": "other",
        "reference": "Definitions and period of sine and cosine",
        "url": "https://dlmf.nist.gov/4.14"
      },
      {
        "label": "CalculatorX mathematical conventions",
        "kind": "other",
        "reference": "Degree default; listed-identity exact values; inverse is Arccos"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Cosine of angle θ"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath 1.4.1 cos (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*",
        "engine": {
          "name": "cos-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": "cos-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 cosine oracle — independent Math.cos + snap",
        "engine": {
          "name": "cos-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤2 ULP scalar comparison vs IUT",
        "engine": {
          "name": "cos-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      }
    ],
    "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node Math.cos). 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": "cos(θ); default degrees; principal inverse on [0°, 180°]"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "deg|rad; textbook snap"
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "angle in; dimensionless out"
    },
    "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": "4/4 legacy golden; 4/4 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "2/2 boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "2 invalid-domain cases"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "≤2 ULP vs O3 applies to the 18 published tabulated vectors (common angles 0°…180° plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including huge angles or unlisted neighborhoods of zeros. Legacy Evidence `tol` is not this policy."
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 declared partitions (cos, invalid-domain, xcal) · 4 golden / 2 boundary unique cases · 2 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 cos; 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 1.0.5 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.5 · 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": "PASS",
      "applicability": "applicable",
      "notes": "angle in → dimensionless cosine (unitless core)"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "3/3 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": "8/8 cross-calculator · xcal-sin-60 PASS vs math.sin; xcal-sin-0 PASS vs math.sin; xcal-sin-33 PASS vs math.sin; xcal-sin-90 PASS vs math.sin; xcal-arccos-half PASS vs math.arccos; xcal-arccos-zero PASS vs math.arccos; xcal-arccos-neg-half PASS vs math.arccos; xcal-arccos-quarter PASS vs math.arccos; xcal-sin-huge-na N/A (sin²θ+cos²θ=1 is not claimed as a binary64 identity for huge angles (e.g. 1e16°) after degree→radian conversion loses phase bits. Those inputs are outside the O3 table and XCAL vectors.); xcal-tan-na N/A (Tan is listed as a related forward-trig tool. It does not encode sin²θ+cos²θ=1 or cos(arccos x)=x.); xcal-arcsin-na N/A (Arcsin is listed as a related inverse-trig tool. It does not encode sin²θ+cos²θ=1 or cos(arccos x)=x; its inverse identity is sin(arcsin 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 18/18 tabulated vectors vs IUT · ≤2 ULP vs O3 applies to the 18 published tabulated vectors (common angles 0°…180° plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including huge angles or unlisted neighborhoods of zeros."
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "expert_reviewed=false"
    }
  },
  "tests": {
    "golden": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "g-cos-60",
        "g-cos-0",
        "g-cos-90",
        "g-cos-33"
      ]
    },
    "boundary": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "missing-theta",
        "theta-abc"
      ]
    },
    "invalid": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "missing-theta",
        "theta-abc"
      ]
    },
    "property": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "prop-range-60",
        "prop-range-0",
        "prop-range-33"
      ],
      "definition_ids": [
        "unit-range"
      ]
    },
    "round_trip": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "rt-60",
        "rt-0",
        "rt-90",
        "rt-33"
      ]
    },
    "metamorphic": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "meta-even-60",
        "meta-even-33",
        "meta-even-15"
      ],
      "definition_ids": [
        "cos-even"
      ]
    },
    "contract": {
      "passed": 1,
      "total": 1,
      "failed": 0
    },
    "cross_interface": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "iface-cos"
      ]
    },
    "cross_calculator": {
      "passed": 8,
      "total": 8,
      "failed": 0,
      "case_ids": [
        "xcal-sin-60",
        "xcal-sin-0",
        "xcal-sin-33",
        "xcal-sin-90",
        "xcal-arccos-half",
        "xcal-arccos-zero",
        "xcal-arccos-neg-half",
        "xcal-arccos-quarter"
      ]
    },
    "ui_integration": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "ui-cos-60",
        "ui-cos-0",
        "ui-cos-33",
        "ui-cos-outside"
      ]
    },
    "o3": {
      "passed": 18,
      "total": 18,
      "failed": 0,
      "case_ids": [
        "o3-cos-0",
        "o3-cos-30",
        "o3-cos-45",
        "o3-cos-60",
        "o3-cos-90",
        "o3-cos-180",
        "o3-cos-33.3",
        "o3-cos-12.5",
        "o3-cos--30",
        "o3-cos-15",
        "o3-cos-rand-00",
        "o3-cos-rand-01",
        "o3-cos-rand-02",
        "o3-cos-rand-03",
        "o3-cos-rand-04",
        "o3-cos-rand-05",
        "o3-cos-rand-06",
        "o3-cos-rand-07"
      ],
      "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 18 published tabulated vectors (common angles 0°…180° plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including huge angles or unlisted neighborhoods of zeros.",
      "reproduce_url": "https://www.calculatorx.com/evidence/math.cos/reproduce"
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "cos",
        "description": "cos(θ)",
        "exercised": true,
        "case_count": 44
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "xcal",
        "description": "Cross-calculator sin²θ+cos²θ=1 vs Sin and cos(arccos x)=x vs Arccos; Tan / Arcsin N/A",
        "exercised": true,
        "case_count": 8
      }
    ]
  },
  "numerical": {
    "representation": "IEEE-754 binary64 Math.cos with textbook snap",
    "tolerance": {
      "type": "ulp",
      "value": 2,
      "rationale": "Independent cos with same exact-angle snap table vs IUT; ≤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 18 published tabulated vectors (common angles 0°…180° plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including huge angles or unlisted neighborhoods of zeros.",
    "max_error_observed": 1,
    "records": [
      {
        "id": "g-cos-60",
        "reference": 0.5,
        "actual": 0.5,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-cos-0",
        "reference": 1,
        "actual": 1,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-cos-90",
        "reference": 0,
        "actual": 0,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-cos-33",
        "reference": 0.8358073613682703,
        "actual": 0.8358073613682703,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-0",
        "reference": 1,
        "actual": 1,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-30",
        "reference": 0.8660254037844386,
        "actual": 0.8660254037844386,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-45",
        "reference": 0.7071067811865476,
        "actual": 0.7071067811865476,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-60",
        "reference": 0.5,
        "actual": 0.5,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-90",
        "reference": 0,
        "actual": 0,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-180",
        "reference": -1,
        "actual": -1,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-33.3",
        "reference": 0.8358073613682703,
        "actual": 0.8358073613682703,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-12.5",
        "reference": 0.9762960071199334,
        "actual": 0.9762960071199334,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos--30",
        "reference": 0.8660254037844386,
        "actual": 0.8660254037844386,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-15",
        "reference": 0.9659258262890683,
        "actual": 0.9659258262890683,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-00",
        "reference": 0.9861128800941029,
        "actual": 0.9861128800941029,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-01",
        "reference": 0.7460184554083706,
        "actual": 0.7460184554083706,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-02",
        "reference": 0.9592943077850056,
        "actual": 0.9592943077850056,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-03",
        "reference": 0.9130070852711516,
        "actual": 0.9130070852711516,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-04",
        "reference": 0.9055265277845048,
        "actual": 0.9055265277845048,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-05",
        "reference": 0.7250555379109475,
        "actual": 0.7250555379109475,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-06",
        "reference": 0.9130364404111473,
        "actual": 0.9130364404111473,
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-cos-rand-07",
        "reference": 0.9875868238749216,
        "actual": 0.9875868238749216,
        "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": "a950247af80dc8f57b508abf82b15712324b3183546b96c850f3ec6173e02b64",
    "evidence_digest": "ece0bdda8ca9515cd122d2544c9f69ccbc9c211a3294389127b1204dd18fcdae",
    "production_sha256": "9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20",
    "attested_catalog_sha256": "e03ef81b30568018b171fd1fc4757c2abe9df7220d9ff35bbaf08038d7630cdb",
    "production_checks": [
      {
        "id": "math.cos:output-const",
        "status": "pass",
        "detail": "output const 1.0.5 vs capability 1.0.5",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.cos:evidence-sha256",
        "status": "pass",
        "detail": "737f1df4efb1",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.cos:semantic-contract",
        "status": "pass",
        "detail": "6/6",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.cos:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.5 vs origin 1.0.5",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.cos:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.cos/1.0.5/2026-09-08.xcal/core/ece0bdda8ca9",
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}