{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "tan",
    "version": "1.0.4",
    "title": "Tangent Calculator",
    "formula_family": "tangent",
    "capability_id": "math.tan",
    "verification_revision": "2026-09-08.policy"
  },
  "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": "tan",
    "version": "1.0.4",
    "uri": "https://www.calculatorx.com/evidence/math.tan/1.0.4.json",
    "verification_revision": "2026-09-08.policy"
  },
  "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": "Trigonometric functions",
        "url": "https://dlmf.nist.gov/4.14"
      },
      {
        "label": "CalculatorX mathematical conventions",
        "kind": "other",
        "reference": "Poles are UNDEFINED, not Infinity; inverse is Arctan"
      }
    ]
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "tan(θ); documented 1e-12° pole classification → UNDEFINED; principal inverse on (−90°, 90°)"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "deg|rad; pole classification / snap / |y| cleanup are documented numerical policies"
    },
    "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": "15/15 legacy golden; 4/4 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "10/10 boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "8 invalid-domain cases"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "≤2 ULP vs O3 applies to the 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, 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 (tan, invalid-domain, xcal) · 15 golden / 10 boundary unique cases · 8 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 tan; 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": "PASS",
      "applicability": "applicable",
      "notes": "angle in → dimensionless tangent (unitless core)"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "5/5 property"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "4/4 metamorphic"
    },
    "CVP-ROUND-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "4/4 round-trips"
    },
    "CVP-XCAL-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "11/11 cross-calculator · xcal-arctan-45 PASS vs math.arctan; xcal-arctan-0 PASS vs math.arctan; xcal-arctan-neg-30 PASS vs math.arctan; xcal-arctan-33 PASS vs math.arctan; xcal-cos-45 PASS vs math.cos; xcal-cos-0 PASS vs math.cos; xcal-cos-neg-30 PASS vs math.cos; xcal-cos-33 PASS vs math.cos; xcal-sin-45 PASS vs math.sin; xcal-sin-30 PASS vs math.sin; xcal-sin-33 PASS vs math.sin; xcal-arctan-huge-na N/A (arctan(tan θ)=θ is not claimed as a binary64 identity for huge angles (e.g. 1e16°) after degree→radian conversion loses phase bits, nor at poles. Those inputs are outside the O3 table and XCAL vectors.); xcal-arcsin-na N/A (Arcsin is listed as a related inverse-trig tool. It does not encode arctan(tan θ)=θ, 1+tan²θ=sec²θ, or 1+cot²θ=csc²θ.)"
    },
    "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 16/16 tabulated vectors vs IUT · ≤2 ULP vs O3 applies to the 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros."
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "expert_reviewed=false"
    }
  },
  "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": "ab920a88aaf27f5e32cc431e7f5f3f327276e0a33a024fd1507fdea295404ca6",
    "evidence_digest": "494caf2c4f61ecefebf48bb718c54af5c4bd5e6f5cf0dff15a07b2d4fbe00926",
    "production_sha256": "9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20",
    "attested_catalog_sha256": "e03ef81b30568018b171fd1fc4757c2abe9df7220d9ff35bbaf08038d7630cdb",
    "production_checks": [
      {
        "id": "math.tan: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.tan:evidence-sha256",
        "status": "pass",
        "detail": "1f4a555a1b14",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.tan:semantic-contract",
        "status": "pass",
        "detail": "25/25",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.tan: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.tan:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.tan/1.0.4/2026-09-08.policy/core/494caf2c4f61",
        "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.tan:cvp-reproduce-manifest-agree",
        "status": "pass",
        "detail": "2026-09-08.policy · efdad939a92a",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.tan: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.tan: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": "tan-engine",
      "version": "1.0.4"
    },
    {
      "name": "tan-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "tan-o3-mpmath-table",
      "version": "math-mpmath-o3"
    },
    {
      "name": "math.arctan",
      "version": "1.0.7",
      "role": "cross_calculator_peer",
      "capability_id": "math.arctan",
      "evidence_digest": "cf317536e8dd9dfcbd1d400e305b97fd335d742afd545e16f3141b246b79466a",
      "evidence": "https://www.calculatorx.com/evidence/math.arctan/1.0.7.cvp.json"
    },
    {
      "name": "math.cos",
      "version": "1.0.5",
      "role": "cross_calculator_peer",
      "capability_id": "math.cos",
      "evidence_digest": "ece0bdda8ca9515cd122d2544c9f69ccbc9c211a3294389127b1204dd18fcdae",
      "evidence": "https://www.calculatorx.com/evidence/math.cos/1.0.5.cvp.json"
    },
    {
      "name": "math.sin",
      "version": "1.0.5",
      "role": "cross_calculator_peer",
      "capability_id": "math.sin",
      "evidence_digest": "f6d93820711850b8f88be0ab287f36990a6f663d1e1ed3c2cd2c88c69409c43e",
      "evidence": "https://www.calculatorx.com/evidence/math.sin/1.0.5.cvp.json"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "00c818a77ba026c2d6aa3f7402680cd2dac2a40a816209600bc3c3fcd0b8921c",
    "attested_at": "2026-09-10T02:52:51.379Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.0.4"
  },
  "timestamps": {
    "verified_at": "2026-09-10T03:41:49.888Z",
    "generated_at": "2026-09-10T03:41:49.888Z"
  },
  "tests": {
    "golden": {
      "passed": 4,
      "total": 4,
      "failed": 0
    },
    "boundary": {
      "passed": 10,
      "total": 10,
      "failed": 0
    },
    "invalid": {
      "passed": 8,
      "total": 8,
      "failed": 0
    },
    "property": {
      "passed": 5,
      "total": 5,
      "failed": 0
    },
    "round_trip": {
      "passed": 4,
      "total": 4,
      "failed": 0
    },
    "metamorphic": {
      "passed": 4,
      "total": 4,
      "failed": 0
    },
    "contract": {
      "passed": 1,
      "total": 1,
      "failed": 0
    },
    "cross_interface": {
      "passed": 1,
      "total": 1,
      "failed": 0
    },
    "cross_calculator": {
      "passed": 11,
      "total": 11,
      "failed": 0
    },
    "ui_integration": {
      "passed": 4,
      "total": 4,
      "failed": 0
    },
    "o3": {
      "passed": 16,
      "total": 16,
      "failed": 0,
      "claim_scope": "≤2 ULP vs O3 applies to the 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros.",
      "max_error_ulp": 1,
      "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee"
    }
  },
  "numerical": {
    "representation": "IEEE-754 binary64 Math.tan with documented snap/cleanup",
    "tolerance": {
      "type": "ulp",
      "value": 2,
      "rationale": "Independent tan with the same documented snap/pole/cleanup policy vs IUT; ≤2 ULP on tabulated O3 vectors, declared a priori. Not a whole-domain ULP guarantee.",
      "declared_before_evaluation": true
    },
    "max_error_observed": 2,
    "claim_scope": "≤2 ULP vs O3 applies to the 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros."
  },
  "coverage": {
    "partitions": [
      {
        "id": "tan",
        "description": "tan(θ)",
        "exercised": true,
        "case_count": 61
      },
      {
        "id": "invalid-domain",
        "description": "Invalid / poles",
        "exercised": true,
        "case_count": 8
      },
      {
        "id": "xcal",
        "description": "Cross-calculator arctan(tan θ)≈θ vs Arctan, 1+tan²θ=sec²θ vs Cos, 1+cot²θ=csc²θ vs Sin; Arcsin N/A",
        "exercised": true,
        "case_count": 11
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Tangent of angle θ"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath 1.4.1 tan (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*",
        "engine": {
          "name": "tan-mpmath-o3",
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "precision_bits": 265,
          "backend": "python",
          "rounding": "round-to-nearest-binary64",
          "independent_of_iut": true,
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee"
        }
      },
      {
        "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": "tan-mpmath-o3",
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "precision_bits": 265,
          "backend": "python",
          "rounding": "round-to-nearest-binary64",
          "independent_of_iut": true,
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee"
        }
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module tangent oracle — independent Math.tan + documented snap/cleanup",
        "engine": {
          "name": "tan-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤2 ULP value comparison vs IUT",
        "engine": {
          "name": "tan-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      }
    ]
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/math.tan/1.0.4.json",
    "evidence_page": "https://www.calculatorx.com/evidence/math.tan/1.0.4",
    "calculator": "https://www.calculatorx.com/calc/math/tan",
    "schema": "https://www.calculatorx.com/developers/cvp/schema/cvp-evidence-1.0.json",
    "protocol": "https://www.calculatorx.com/developers/cvp/spec/1.0",
    "manifest": "https://www.calculatorx.com/evidence/math.tan/1.0.4.cvp.json",
    "manifest_immutable": "https://www.calculatorx.com/evidence/math.tan/1.0.4/2026-09-08.policy.cvp.json",
    "reproduce": "https://www.calculatorx.com/evidence/math.tan/reproduce"
  },
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}