{ "protocol": { "name": "CVP", "version": "1.0.0-proposed", "revision": "2026-09-13", "spec_sha256": "f62725968356c92930531cd6085db76e216da06e95be53d636b0d2cf3218b148", "spec": "https://www.calculatorx.com/developers/cvp/spec/1.0" }, "document_status": "proposed", "calculator": { "id": "arctan", "version": "1.0.9", "title": "Arctangent Calculator", "formula_family": "arctan", "capability_id": "math.arctan", "verification_revision": "2026-10-16.inverse-trig-discovery-pins-v8" }, "profile": "core", "status": "VERIFIED", "verification_status": "VERIFIED", "production_freshness": "CURRENT", "overall_trust": "VERIFIED", "runner": { "name": "cvp-runner", "version": "1.0.0" }, "environment": { "runtime": "node", "runtime_version": "22.20.0", "numeric_model": "IEEE-754 binary64", "os": "darwin" }, "suite": { "id": "arctan", "version": "1.0.9", "uri": "https://www.calculatorx.com/evidence/math.arctan/1.0.9.json", "verification_revision": "2026-10-16.inverse-trig-discovery-pins-v8" }, "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" } ] }, "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 CVP boundary · 3/3 legacy Evidence 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 legacy golden / 3 CVP boundary unique cases · 3 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "6/6 CVP contract · release-artifacts-aligned=PASS · schema-output-required-declared=PASS · schema-valid-input-executes=PASS · engine-success-output-validates-schema=PASS · schema-rejects-incomplete-input=PASS · rest-success-payload-validates-schema=PASS" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine arctan; Node binary64" }, "CVP-ART-01": { "result": "PASS", "applicability": "required", "notes": "release_integrity.status=verified · digests: artifact_evidence_sha256=Evidence core (Trust freshness) · cvp_evidence_digest=artifacts.evidence_digest (fingerprint v2) · evidence_bundle_sha256=legacy Evidence JSON bytes · evidence_catalog_digest=attested_catalog_sha256 · production_sha256=bound production report · see artifacts.digest_registry" }, "CVP-PROD-01": { "result": "PASS", "applicability": "required", "notes": "this calculator CURRENT · bound snapshot pass @ 2026-10-16T09:32:20.710Z · live site-wide report stale @ 2026-10-16T09:32:34.525Z (2 other capabilities) · local checks pass · attestation_id=225a9b2332c314cc19dabe95ce6f9a3d114baa053f5d2a5648e38b0f61d70b54 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-16T09:32:20.710Z · Live production status STALE (2 capabilities; 374 remain CURRENT) @ 2026-10-16T09:32:34.525Z · Public schema 1.0.9 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.9 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-latest-alias-agrees=pass · cvp-immutable-manifest-fetch=pass · cvp-immutable-manifest-sha256=pass · cvp-latest-alias-matches-immutable=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=22a9c6e652dd62b437a96ba5727dcc859557ad1afbc6f77c5709fbe1a0e0cdc6 · verified_at=2026-10-16T08:57:04.842Z · evidence_attested_at=2026-10-16T08:57:04.842Z · last_confirmed_current_at=2026-10-16T09:32:20.710Z · rendered_at=2026-10-16T09:32:34.867Z · binds=cvp_core_sha256", "check_result": "PASS", "production_state": "CURRENT", "binding_current": true }, "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 21/21. Error-path engine·REST·MCP 5/5 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity." }, "CVP-ORACLE-01": { "result": "PASS", "applicability": "higher_assurance", "notes": "O3 21/21 tabulated vectors vs IUT" }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "named expert review not performed" } }, "interfaces": { "compared": [ "ui-ssr", "rest", "mcp", "ui-url-result-graph" ], "result": "PASS", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). Success 21/21. Error-path engine·REST·MCP 5/5 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity." }, "artifacts": { "evidence_bundle_sha256": "2bf56da4343a9a0e384051bd00b7e4ca23011692d2d21ea574275094dc994b3f", "evidence_digest": "4fb2a8fe2cc514635a6c9c25b4cfd01f2aa897933dcd958305d1429771da75ba", "production_sha256": "22a9c6e652dd62b437a96ba5727dcc859557ad1afbc6f77c5709fbe1a0e0cdc6", "attested_catalog_sha256": "643307717b1fa27fe4caf33724622385431ef672637168cdea4a5005944d7106", "production_checks": [ { "id": "math.arctan:output-const", "status": "pass", "detail": "output const 1.0.9 vs capability 1.0.9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" }, { "id": "math.arctan:evidence-sha256", "status": "pass", "detail": "297a45a4e22f", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" }, { "id": "math.arctan:semantic-contract", "status": "pass", "detail": "10/10", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" }, { "id": "math.arctan:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.0.9 vs origin 1.0.9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" }, { "id": "math.arctan:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.arctan/1.0.9/2026-10-16.inverse-trig-discovery-pins-v8/core/4fb2a8fe2cc5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z", "projection_compared": false }, { "id": "math.arctan:cvp-latest-alias-agrees", "status": "pass", "detail": "math.arctan/1.0.9/2026-10-16.inverse-trig-discovery-pins-v8/core/4fb2a8fe2cc5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z", "projection_compared": false }, { "id": "math.arctan:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" }, { "id": "math.arctan:cvp-immutable-manifest-sha256", "status": "pass", "detail": "4fb2a8fe2cc5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" }, { "id": "math.arctan:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.arctan/1.0.9/2026-10-16.inverse-trig-discovery-pins-v8/core/4fb2a8fe2cc5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z", "projection_compared": false }, { "id": "math.arctan:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" }, { "id": "math.arctan:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-16T08:57:04.842Z" } ], "digest_registry": { "digest_algorithm": "sha256", "canonicalization": "json-sorted-keys-utf8", "entries": [ { "name": "cvp_core_sha256", "field": "artifacts.cvp_core_sha256", "digest_scope": "cvp_verification_fingerprint_v2", "value": "4fb2a8fe2cc514635a6c9c25b4cfd01f2aa897933dcd958305d1429771da75ba", "note": "Immutable verification core; excludes attestation/live-status and Evidence contract counts" }, { "name": "cvp_evidence_digest", "field": "artifacts.evidence_digest", "digest_scope": "cvp_verification_fingerprint_v2", "value": "4fb2a8fe2cc514635a6c9c25b4cfd01f2aa897933dcd958305d1429771da75ba", "note": "Alias of cvp_core_sha256 (historical field name)" }, { "name": "artifact_evidence_sha256", "field": "release_integrity.digests.evidence_core_sha256", "digest_scope": "evidence_artifact_core", "value": "297a45a4e22f6831271398357071d61899fd91bf9525f736682e826e17b67f24", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "643307717b1fa27fe4caf33724622385431ef672637168cdea4a5005944d7106", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "4fb2a8fe2cc514635a6c9c25b4cfd01f2aa897933dcd958305d1429771da75ba" }, "dependencies": [ { "name": "arctan-engine", "version": "1.0.9" }, { "name": "arctan-reference-oracle", "version": "1.0.0" }, { "name": "arctan-o3-mpmath-table", "version": "math-mpmath-o3" }, { "name": "math.tan", "version": "1.0.4", "role": "cross_calculator_peer", "capability_id": "math.tan", "evidence_digest": "494caf2c4f61ecefebf48bb718c54af5c4bd5e6f5cf0dff15a07b2d4fbe00926", "evidence": "https://www.calculatorx.com/evidence/math.tan/1.0.4.cvp.json" }, { "name": "node", "version": "22.20.0" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "225a9b2332c314cc19dabe95ce6f9a3d114baa053f5d2a5648e38b0f61d70b54", "attested_at": "2026-10-16T08:57:04.842Z", "last_confirmed_current_at": "2026-10-16T09:32:20.710Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-10-16T09:32:20.710Z", "live_updated_at": "2026-10-16T09:32:34.525Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-10-16T09:32:20.710Z", "site_stale_count": 2 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 2, "site_stale_capability_count": 2, "evidence_attested_at": "2026-10-16T08:57:04.842Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.0.9", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-16T08:57:04.842Z", "generated_at": "2026-10-16T08:57:04.842Z", "rendered_at": "2026-10-16T09:32:34.867Z", "notes": "verified_at/generated_at mark the first publication of this cvp_core_sha256 (artifacts.evidence_digest alias) for suite verification. evidence_attested_at/attested_at is the first production bind of that core digest. last_confirmed_current_at is the latest site-wide report that still confirms CURRENT. rendered_at is this JSON serialization and is not part of cvp_core_sha256 / evidence_digest. Production attestation binds cvp_core_sha256 (binds evidence_digest). Causal order: verified_at ≤ evidence_attested_at ≤ last_confirmed_current_at. attestation.bound_snapshot.site_stale_count is the site-wide stale capability count at Manifest bind time — not a live value. Fetch attestation.live_site_status.href for the current site report." }, "tests": { "golden": { "passed": 9, "total": 9, "failed": 0 }, "boundary": { "passed": 3, "total": 3, "failed": 0 }, "invalid": { "passed": 3, "total": 3, "failed": 0 }, "property": { "passed": 8, "total": 8, "failed": 0 }, "round_trip": { "passed": 4, "total": 4, "failed": 0 }, "metamorphic": { "passed": 3, "total": 3, "failed": 0 }, "contract": { "passed": 6, "total": 6, "failed": 0 }, "cross_interface": { "passed": 31, "total": 31, "failed": 0 }, "cross_calculator": { "passed": 4, "total": 4, "failed": 0 }, "ui_integration": { "passed": 4, "total": 4, "failed": 0 }, "o3": { "passed": 21, "total": 21, "failed": 0, "max_error_ulp": 1, "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee" } }, "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 reference vs IUT; ≤2 ULP on both deg and rad. Canonical values are not display-flushed. Declared a priori.", "declared_before_evaluation": true }, "max_error_observed": 1 }, "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 } ] }, "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", "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 deg; ≤2 ULP on tabulated vectors only, not the whole domain. Distinct from legacy Evidence case-level tol.", "engine": { "name": "atan-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 arctan oracle — independent Math.atan + snap", "engine": { "name": "arctan-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_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, "same_runtime_as_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.arctan/1.0.9.json", "evidence_page": "https://www.calculatorx.com/evidence/math.arctan/1.0.9", "calculator": "https://www.calculatorx.com/calc/math/arctan", "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.arctan/1.0.9.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.arctan/1.0.9/2026-10-16.inverse-trig-discovery-pins-v8.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.arctan/1.0.9/2026-10-16.inverse-trig-discovery-pins-v8.4fb2a8fe2cc5.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }