{ "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": "complex", "version": "1.1.0", "title": "Complex Number Calculator", "formula_family": "complex", "capability_id": "math.complex", "verification_revision": "2026-09-22.vector-la-cvp" }, "profile": "core", "verified_scope": "all published modes", "status": "VERIFIED", "verification_status": "VERIFIED", "production_freshness": "CURRENT", "overall_trust": "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": "complex", "version": "1.1.0", "uri": "https://www.calculatorx.com/evidence/math.complex/1.1.0.json", "verification_revision": "2026-09-22.vector-la-cvp" }, "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-XCAL-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "ISO 80000-2:2019 Quantities and units — Mathematics", "kind": "standard", "reference": "Complex number z = re + im i, modulus, and argument" }, { "label": "CRC Standard Mathematical Tables — De Moivre and Euler form", "kind": "other", "reference": "z^n = r^n (cos nθ + i sin nθ); z = r e^{iθ}; nth roots equally spaced on a circle" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "Unrounded O2 hypot/atan2 and De Moivre vs IUT roundSmart; rectangular and polar forms" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Not a CAS, not contour integrals, not i^i. Discovery /complex-polar, /complex-power, /complex-roots, /complex-euler lock one mode." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O2 expected_values + O2 numerical_behavior" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "6/6 legacy golden; 11/11 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "3/3 numeric-edge Evidence + 2/2 near-singularity numeric; illegal enum/system is Invalid only" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "4 Evidence illegal-input + 5/5 oracle-backed error-code (exact_error_match, not ULP)" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "max_error_observed_ulp=0; policy declared a priori" }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "12/12 declared partitions (add, sub, mul, div, rect-to-polar, polar-to-rect, conjugate, modulus, power, root, euler, invalid-domain) · 6 legacy golden / 5 CVP boundary unique cases · 4 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "5/5 CVP contract · release-artifacts-aligned=PASS · schema-output-required-declared=PASS · schema-valid-input-executes=PASS · engine-success-output-validates-schema=PASS · rest-success-payload-validates-schema=PASS" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine complex; 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 @ 2026-09-22T04:01:06.903Z · live site-wide report stale @ 2026-09-22T04:01:09.801Z (13 other capabilities) · local checks pass · attestation_id=2215e43bd5546922b9b7142484b40765c775fc3ae5e41ddad6f42d09a93ba13b · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-09-22T04:01:06.903Z · Live production status STALE (13 capabilities; 176 remain CURRENT) @ 2026-09-22T04:01:09.801Z · 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=ab66486c562fc7c8f16c9af1e1fa18208ecc7410ff0a33a12be34f8ad968b22b · verified_at=2026-09-22T03:02:51.070Z · evidence_attested_at=2026-09-22T03:02:51.070Z · last_confirmed_current_at=2026-09-22T04:01:06.903Z · rendered_at=2026-09-22T04:01:09.852Z · binds=cvp_core_sha256", "check_result": "PASS", "production_state": "CURRENT", "binding_current": true }, "CVP-DIM-01": { "result": "PASS", "applicability": "applicable", "notes": "complex plane" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "3/3 property · enumerated fixed assertions (not generated; no seed)" }, "CVP-META-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "No input→output transformation vectors in pack — control not in obligation set" }, "CVP-ROUND-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "No inverse / round-trip vectors in pack — control not in obligation set" }, "CVP-XCAL-01": { "result": "PASS", "applicability": "applicable", "notes": "2/2 cross-calculator · xcal-mod-pythagorean PASS vs math.pythagorean; xcal-pow-mul PASS vs math.complex" }, "CVP-IFACE-01": { "result": "PASS", "applicability": "applicable", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (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." }, "CVP-ORACLE-01": { "result": "SKIP", "applicability": "higher_assurance", "notes": "O2 present; O3 not required this wave" }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "named expert review not performed" } }, "interfaces": { "compared": [ "ui-ssr", "rest", "mcp" ], "result": "PASS", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (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." }, "artifacts": { "evidence_bundle_sha256": "60fe099e820c229eab9d9514cbc67ed4c4ac59abcb2dd8f38865fac0dcd5c88b", "evidence_digest": "403fe3cb25d56d21475a6ea244ab1c17e8c7e753f7c14afe0d78316825456ff1", "production_sha256": "ab66486c562fc7c8f16c9af1e1fa18208ecc7410ff0a33a12be34f8ad968b22b", "attested_catalog_sha256": "e00979a0a41218268bfef843cbca86f27d9855fac81f401e5f9defefca4b39ef", "production_checks": [ { "id": "math.complex: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": "2026-09-22T03:02:51.070Z" }, { "id": "math.complex:evidence-sha256", "status": "pass", "detail": "8d86519defbd", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z" }, { "id": "math.complex:semantic-contract", "status": "pass", "detail": "18/18", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z" }, { "id": "math.complex: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": "2026-09-22T03:02:51.070Z" }, { "id": "math.complex:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.complex/1.1.0/2026-09-22.vector-la-cvp/core/403fe3cb25d5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z", "projection_compared": false }, { "id": "math.complex:cvp-latest-alias-agrees", "status": "pass", "detail": "math.complex/1.1.0/2026-09-22.vector-la-cvp/core/403fe3cb25d5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z", "projection_compared": false }, { "id": "math.complex:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z" }, { "id": "math.complex:cvp-immutable-manifest-sha256", "status": "pass", "detail": "403fe3cb25d5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z" }, { "id": "math.complex:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.complex/1.1.0/2026-09-22.vector-la-cvp/core/403fe3cb25d5", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z", "projection_compared": false }, { "id": "math.complex:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z" }, { "id": "math.complex:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-22T03:02:51.070Z" } ], "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": "403fe3cb25d56d21475a6ea244ab1c17e8c7e753f7c14afe0d78316825456ff1", "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": "403fe3cb25d56d21475a6ea244ab1c17e8c7e753f7c14afe0d78316825456ff1", "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": "8d86519defbdf5e2fab11d45e22c593c9d950b0ccc7101b95f61e07caa08123b", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "e00979a0a41218268bfef843cbca86f27d9855fac81f401e5f9defefca4b39ef", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "403fe3cb25d56d21475a6ea244ab1c17e8c7e753f7c14afe0d78316825456ff1" }, "dependencies": [ { "name": "complex-engine", "version": "1.1.0" }, { "name": "complex-reference-oracle", "version": "1.0.0" }, { "name": "math.pythagorean", "version": "1.1.2", "role": "cross_calculator_peer", "capability_id": "math.pythagorean", "evidence_digest": "4847c211167ff972b8497a233e0140af9e7dd6806308756a46c10634992aea1c", "evidence": "https://www.calculatorx.com/evidence/math.pythagorean/1.1.2.cvp.json" }, { "name": "math.complex", "version": "1.1.0", "role": "cross_calculator_peer", "capability_id": "math.complex", "evidence_digest": "403fe3cb25d56d21475a6ea244ab1c17e8c7e753f7c14afe0d78316825456ff1", "evidence": "https://www.calculatorx.com/evidence/math.complex/1.1.0.cvp.json" }, { "name": "node", "version": "20.19.2" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "2215e43bd5546922b9b7142484b40765c775fc3ae5e41ddad6f42d09a93ba13b", "attested_at": "2026-09-22T03:02:51.070Z", "last_confirmed_current_at": "2026-09-22T04:01:06.903Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-09-22T04:01:06.903Z", "live_updated_at": "2026-09-22T04:01:09.801Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-09-22T04:01:06.903Z", "site_stale_count": 13 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 13, "site_stale_capability_count": 13, "evidence_attested_at": "2026-09-22T03:02:51.070Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.1.0", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-09-22T03:02:51.070Z", "generated_at": "2026-09-22T03:02:51.070Z", "rendered_at": "2026-09-22T04:01:09.852Z", "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": 11, "total": 11, "failed": 0 }, "boundary": { "passed": 5, "total": 5, "failed": 0 }, "invalid": { "passed": 9, "total": 9, "failed": 0, "comparison": "exact_error_match" }, "property": { "passed": 3, "total": 3, "failed": 0, "kind": "fixed" }, "round_trip": { "passed": 0, "total": 0, "failed": 0 }, "metamorphic": { "passed": 0, "total": 0, "failed": 0 }, "contract": { "passed": 5, "total": 5, "failed": 0 }, "cross_interface": { "passed": 5, "total": 5, "failed": 0 }, "cross_calculator": { "passed": 2, "total": 2, "failed": 0 } }, "numerical": { "representation": "IEEE-754 binary64 complex arithmetic; IUT publishes toPrecision(12) / roundSmart", "tolerance": { "type": "relative", "value": 1e-10, "rationale": "O2 is unrounded hypot/atan2 and De Moivre. IUT publishes 12 significant digits. Relative 1e-10 covers presentation rounding; declared a priori.", "declared_before_evaluation": true }, "max_error_observed": 0 }, "coverage": { "partitions": [ { "id": "add", "description": "add", "exercised": true, "case_count": 10 }, { "id": "sub", "description": "sub", "exercised": true, "case_count": 1 }, { "id": "mul", "description": "mul", "exercised": true, "case_count": 2 }, { "id": "div", "description": "div", "exercised": true, "case_count": 1 }, { "id": "rect-to-polar", "description": "rect_to_polar", "exercised": true, "case_count": 2 }, { "id": "polar-to-rect", "description": "polar_to_rect", "exercised": true, "case_count": 1 }, { "id": "conjugate", "description": "conjugate", "exercised": true, "case_count": 2 }, { "id": "modulus", "description": "modulus", "exercised": true, "case_count": 3 }, { "id": "power", "description": "power", "exercised": true, "case_count": 5 }, { "id": "root", "description": "root", "exercised": true, "case_count": 3 }, { "id": "euler", "description": "euler", "exercised": true, "case_count": 2 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 9 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "z = re + im i; r = |z|; De Moivre z^n and nth roots" }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module complex oracle — unrounded rectangular/polar identities and De Moivre powers/roots (same runtime as IUT; not IUT transcription)", "engine": { "name": "complex-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 unrounded hypot/atan2 vs IUT roundSmart — relative 1e-10 / 16 pub ULP", "engine": { "name": "complex-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.complex/1.1.0.json", "evidence_page": "https://www.calculatorx.com/evidence/math.complex/1.1.0", "calculator": "https://www.calculatorx.com/calc/math/complex-number", "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.complex/1.1.0.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.complex/1.1.0/2026-09-22.vector-la-cvp.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.complex/1.1.0/2026-09-22.vector-la-cvp.403fe3cb25d5.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }