{ "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": "arccos", "version": "1.1.0", "title": "Arccosine Calculator", "formula_family": "arccos", "capability_id": "math.arccos", "verification_revision": "2026-10-29.math-uuce-fields-v1" }, "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": "arccos", "version": "1.1.0", "uri": "https://www.calculatorx.com/evidence/math.arccos/1.1.0.json", "verification_revision": "2026-10-29.math-uuce-fields-v1" }, "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-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 algebraic values only for exact inputs" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "principal arccos(x) on [0, π]" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "x ∈ [−1, 1]; principal range [0, π]" }, "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": "5/5 legacy golden; 9/9 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "5/5 CVP boundary · 5/5 legacy Evidence boundary" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "5 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": "2/2 declared partitions (arccos, invalid-domain) · 5 legacy golden / 5 CVP boundary unique cases · 5 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 arccos; 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 @ 2026-10-29T09:50:17.083Z · live site-wide report stale @ 2026-10-29T09:50:57.852Z (11 other capabilities) · local checks pass · attestation_id=40e7a05dc161e4cce7ce61ca2a18e81e0b12b04c3bbf14a62ec111a05f943e8f · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-29T09:50:17.083Z · Live production status STALE (11 capabilities; 365 remain CURRENT) @ 2026-10-29T09:50:57.852Z · Public schema 1.1.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.1.0 · 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=04247b6c380c165c9aed6d75d9a913ff0febd08ce53bc1aeb7bf561a0dc53e62 · verified_at=2026-10-29T09:10:49.640Z · evidence_attested_at=2026-10-29T09:10:49.640Z · last_confirmed_current_at=2026-10-29T09:50:17.083Z · rendered_at=2026-10-29T09:50:58.166Z · 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": "4/4 metamorphic" }, "CVP-ROUND-01": { "result": "PASS", "applicability": "applicable", "notes": "5/5 round-trips" }, "CVP-XCAL-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "No related calculator in the same formula family / no related-identity peers declared — control not in obligation set" }, "CVP-IFACE-01": { "result": "PASS", "applicability": "applicable", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). Success 30/30. Error-path engine·REST·MCP 7/7 (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 30/30 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 30/30. Error-path engine·REST·MCP 7/7 (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": "8d02eadcb369d086838c1abb7bff5fe3f6eb67ff70a1b95b1c1bbbca5859b96b", "evidence_digest": "9dd654d8b9fbb55f26f93c374e828feb8c7da73fa91d18bfe587af6b05028cd3", "production_sha256": "04247b6c380c165c9aed6d75d9a913ff0febd08ce53bc1aeb7bf561a0dc53e62", "attested_catalog_sha256": "0ae84cdda4265706da5640db58e61e30e0a60e16c65f8eaba247dd5f28369b16", "production_checks": [ { "id": "math.arccos:output-const", "status": "pass", "detail": "output const 1.1.0 vs capability 1.1.0", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" }, { "id": "math.arccos:evidence-sha256", "status": "pass", "detail": "62def4c2fe5e", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" }, { "id": "math.arccos:semantic-contract", "status": "pass", "detail": "10/10", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" }, { "id": "math.arccos:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.1.0 vs origin 1.1.0", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" }, { "id": "math.arccos:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.arccos/1.1.0/2026-10-29.math-uuce-fields-v1/core/9dd654d8b9fb", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z", "projection_compared": false }, { "id": "math.arccos:cvp-latest-alias-agrees", "status": "pass", "detail": "math.arccos/1.1.0/2026-10-29.math-uuce-fields-v1/core/9dd654d8b9fb", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z", "projection_compared": false }, { "id": "math.arccos:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" }, { "id": "math.arccos:cvp-immutable-manifest-sha256", "status": "pass", "detail": "9dd654d8b9fb", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" }, { "id": "math.arccos:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.arccos/1.1.0/2026-10-29.math-uuce-fields-v1/core/9dd654d8b9fb", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z", "projection_compared": false }, { "id": "math.arccos:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" }, { "id": "math.arccos:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-29T09:10:49.640Z" } ], "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": "9dd654d8b9fbb55f26f93c374e828feb8c7da73fa91d18bfe587af6b05028cd3", "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": "9dd654d8b9fbb55f26f93c374e828feb8c7da73fa91d18bfe587af6b05028cd3", "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": "62def4c2fe5e0ecf5f174eca5c822902ab1dfc407db88fa1e525c33704fc4bf9", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "0ae84cdda4265706da5640db58e61e30e0a60e16c65f8eaba247dd5f28369b16", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "9dd654d8b9fbb55f26f93c374e828feb8c7da73fa91d18bfe587af6b05028cd3" }, "dependencies": [ { "name": "arccos-engine", "version": "1.1.0" }, { "name": "arccos-reference-oracle", "version": "1.0.0" }, { "name": "arccos-o3-mpmath-table", "version": "arccos-mpmath-o3" }, { "name": "node", "version": "22.20.0" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "40e7a05dc161e4cce7ce61ca2a18e81e0b12b04c3bbf14a62ec111a05f943e8f", "attested_at": "2026-10-29T09:10:49.640Z", "last_confirmed_current_at": "2026-10-29T09:50:17.083Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-10-29T09:50:17.083Z", "live_updated_at": "2026-10-29T09:50:57.852Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-10-29T09:50:17.083Z", "site_stale_count": 11 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 11, "site_stale_capability_count": 11, "evidence_attested_at": "2026-10-29T09:10:49.640Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.1.0", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-29T09:10:49.640Z", "generated_at": "2026-10-29T09:10:49.640Z", "rendered_at": "2026-10-29T09:50:58.166Z", "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": 5, "total": 5, "failed": 0 }, "invalid": { "passed": 5, "total": 5, "failed": 0 }, "property": { "passed": 8, "total": 8, "failed": 0 }, "round_trip": { "passed": 5, "total": 5, "failed": 0 }, "metamorphic": { "passed": 4, "total": 4, "failed": 0 }, "contract": { "passed": 6, "total": 6, "failed": 0 }, "cross_interface": { "passed": 42, "total": 42, "failed": 0 }, "ui_integration": { "passed": 4, "total": 4, "failed": 0 }, "o3": { "passed": 30, "total": 30, "failed": 0, "max_error_ulp": 2 } }, "numerical": { "representation": "IEEE-754 binary64 Math.acos with textbook snap (IUT)", "tolerance": { "type": "ulp", "value": 2, "rationale": "CVP acceptance is ≤2 ULP on both deg and rad vs independent reference, declared a priori. O3 (mpmath table; historical backend not recorded) is the numerical expected-value source when the input is tabulated; O2 (separate-module Math.acos + snap) covers live identities. Legacy Evidence case-level `tol` (e.g. 1e-8 on no-near-exact-snap) is a regression epsilon and is not this policy.", "declared_before_evaluation": true }, "max_error_observed": 2 }, "coverage": { "partitions": [ { "id": "arccos", "description": "arccos(x) in [−1, 1]", "exercised": true, "case_count": 61 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 5 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Principal inverse cosine (NIST DLMF §4.23)" }, { "class": "O3", "reference_scope": "expected_values", "scope": "expected_values", "label": "Precomputed mpmath arccos (80 dps) rounded to nearest binary64; historical backend not recorded — not Node Math.acos", "engine": { "name": "arccos-mpmath-o3", "library": "mpmath 1.4.1", "mpmath_dps": 80, "precision_bits": 265, "backend": "not_recorded", "rounding": "round-to-nearest-binary64", "independent_of_iut": true, "same_runtime_as_iut": false, "generator_version": "1.0.0" } }, { "class": "O3", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O3 table vs IUT deg; ≤2 ULP. Distinct from legacy Evidence case-level tol.", "engine": { "name": "arccos-mpmath-o3", "library": "mpmath 1.4.1", "mpmath_dps": 80, "precision_bits": 265, "backend": "not_recorded", "rounding": "round-to-nearest-binary64", "independent_of_iut": true, "same_runtime_as_iut": false, "generator_version": "1.0.0" } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module arccos oracle — independent Math.acos + snap (shares Node/V8 binary64)", "engine": { "name": "arccos-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "O2 binary64 path for live identities; ULP claims vs IUT prefer O3 when tabulated", "engine": { "name": "arccos-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.arccos/1.1.0.json", "evidence_page": "https://www.calculatorx.com/evidence/math.arccos/1.1.0", "calculator": "https://www.calculatorx.com/calc/math/arccos", "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.arccos/1.1.0.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.arccos/1.1.0/2026-10-29.math-uuce-fields-v1.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.arccos/1.1.0/2026-10-29.math-uuce-fields-v1.9dd654d8b9fb.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }