{ "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": "lcm", "version": "1.0.4", "title": "LCM Calculator", "formula_family": "lcm", "capability_id": "math.lcm", "verification_revision": "2026-10-21.lcm-complete-contract-v2" }, "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": "exact_integer", "os": "darwin" }, "suite": { "id": "lcm", "version": "1.0.4", "uri": "https://www.calculatorx.com/evidence/math.lcm/1.0.4.json", "verification_revision": "2026-10-21.lcm-complete-contract-v2" }, "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-PROP-01", "CVP-META-01", "CVP-XCAL-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "Encyclopedia of Mathematics — Least common multiple", "kind": "other", "reference": "Definition; pairwise fold; relation to GCD", "url": "https://encyclopediaofmath.org/wiki/Least_common_multiple" }, { "label": "Python math.lcm — zero convention", "kind": "other", "reference": "If any argument is zero, LCM = 0", "url": "https://docs.python.org/3/library/math.html#math.lcm" }, { "label": "CalculatorX integer convention", "kind": "other", "reference": "Absolute value; 48-digit BigInt domain; divide-first identity" }, { "label": "MIT Mathematics for Computer Science — Chapter 8: Number Theory", "kind": "other", "reference": "Chapter 8, including sections 8.2–8.9 and problem 8.24", "url": "https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-spring-2015/mit6_042js15_textbook.pdf" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "LCM(a,b)=|a/GCF(a,b)×b|; exact_integer / BigInt / exact_equality" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "2–32 signed integers,48 digits each, strict matching aliases, complete exact result/work; any zero→0; bounded listing and prime checks" }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless integer" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O2 expected_values/numerical_behavior (|a/GCF×b| dual-checked against prime-power when factorable; exact_equality; same_runtime_as_iut)" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "6/6 legacy golden; 9/9 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "7/7 CVP boundary · 7/7 legacy Evidence boundary" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "3 invalid-domain cases" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "exact_integer · BigInt · exact_equality (actual exact decimal string === independent oracle exact decimal string); mismatches=0; ULP not applicable" }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "8/8 declared partitions (lcm, zero, negative, beyond-safe-integer, multi-input-fold, method-unavailable, xcal, invalid-domain) · 6 legacy golden / 7 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 lcm; exact_integer BigInt (IUT/O2). Node is a runtime dependency, not the numeric model" }, "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 @ 2026-10-21T08:37:00.433Z · live site-wide report stale @ 2026-10-21T08:37:16.301Z (5 other capabilities) · local checks pass · attestation_id=cb614f6316a4a99e61eb83d940f937a7c264e05cb52f3e289bd091d67fdff824 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-21T08:37:00.433Z · Live production status STALE (5 capabilities; 371 remain CURRENT) @ 2026-10-21T08:37:16.301Z · 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-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=7c83e318abf41b280fd1a6c860fa53b512cf36456702de13f93c9f6aaf70ab30 · verified_at=2026-10-21T03:34:38.635Z · evidence_attested_at=2026-10-21T03:34:38.635Z · last_confirmed_current_at=2026-10-21T08:37:00.433Z · rendered_at=2026-10-21T08:37:16.660Z · binds=cvp_core_sha256", "check_result": "PASS", "production_state": "CURRENT", "binding_current": true }, "CVP-DIM-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "Unitless core calculator — no physical dimension algebra" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "3/3 property" }, "CVP-META-01": { "result": "PASS", "applicability": "applicable", "notes": "1/1 metamorphic" }, "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": "5/5 cross-calculator · xcal-gcf-8-12 PASS vs math.gcf; xcal-gcf-18-27 PASS vs math.gcf; xcal-gcf-coprime PASS vs math.gcf; xcal-gcf-neg PASS vs math.gcf; xcal-gcf-bigint-unsafe PASS vs math.gcf; xcal-gcf-all-zero-na N/A (GCF(a,b)·LCM(a,b)=|ab| is claimed for nonzero integers. GCF(0,0) is undefined, so the identity is not evaluated on the all-zero set.); xcal-fractions-na N/A (Fractions is listed as a related tool because LCD/GCF appear in reduction. It does not encode GCF(a,b)·LCM(a,b)=|ab| as a peer identity on this calculator.); xcal-factorial-na N/A (Factorial is listed as a related integer tool. It does not encode GCF(a,b)·LCM(a,b)=|ab|.); xcal-division-na N/A (Division is listed as a related tool. It does not encode GCF(a,b)·LCM(a,b)=|ab|.)" }, "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." }, "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." }, "artifacts": { "evidence_bundle_sha256": "2e5c76dd6eb37222d2ab90e6d5b76d83271acd604cf605a3bb4af223ecd0ab09", "evidence_digest": "f87d285d6b3e531f6d8d3e0ea18fa0d381e613a9a303d98693c2bf918470255a", "production_sha256": "7c83e318abf41b280fd1a6c860fa53b512cf36456702de13f93c9f6aaf70ab30", "attested_catalog_sha256": "9b96a2c8fbf62a8306adee80ae161d6b6eeb7d64addac11a3cc4670eb22d2635", "production_checks": [ { "id": "math.lcm: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": "2026-10-21T03:34:38.635Z" }, { "id": "math.lcm:evidence-sha256", "status": "pass", "detail": "22ee8ca8d9cd", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z" }, { "id": "math.lcm:semantic-contract", "status": "pass", "detail": "20/20", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z" }, { "id": "math.lcm: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": "2026-10-21T03:34:38.635Z" }, { "id": "math.lcm:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.lcm/1.0.4/2026-10-21.lcm-complete-contract-v2/core/f87d285d6b3e", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z", "projection_compared": false }, { "id": "math.lcm:cvp-latest-alias-agrees", "status": "pass", "detail": "math.lcm/1.0.4/2026-10-21.lcm-complete-contract-v2/core/f87d285d6b3e", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z", "projection_compared": false }, { "id": "math.lcm:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z" }, { "id": "math.lcm:cvp-immutable-manifest-sha256", "status": "pass", "detail": "f87d285d6b3e", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z" }, { "id": "math.lcm:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.lcm/1.0.4/2026-10-21.lcm-complete-contract-v2/core/f87d285d6b3e", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z", "projection_compared": false }, { "id": "math.lcm:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z" }, { "id": "math.lcm:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-21T03:34:38.635Z" } ], "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": "f87d285d6b3e531f6d8d3e0ea18fa0d381e613a9a303d98693c2bf918470255a", "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": "f87d285d6b3e531f6d8d3e0ea18fa0d381e613a9a303d98693c2bf918470255a", "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": "22ee8ca8d9cdca7ef1f6f2fae8be0d27207f17bb7be5cb3cb12fc08c0c75a629", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "9b96a2c8fbf62a8306adee80ae161d6b6eeb7d64addac11a3cc4670eb22d2635", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "f87d285d6b3e531f6d8d3e0ea18fa0d381e613a9a303d98693c2bf918470255a" }, "dependencies": [ { "name": "lcm-engine", "version": "1.0.4" }, { "name": "lcm-reference-oracle", "version": "1.0.0" }, { "name": "math.gcf", "version": "1.0.3", "role": "cross_calculator_peer", "capability_id": "math.gcf", "evidence_digest": "9af66f58265fbeebc60d298170d7d652bf6fad30183addcac1b7f39ce2e6b6d0", "evidence": "https://www.calculatorx.com/evidence/math.gcf/1.0.3.cvp.json" }, { "name": "node", "version": "22.20.0" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "cb614f6316a4a99e61eb83d940f937a7c264e05cb52f3e289bd091d67fdff824", "attested_at": "2026-10-21T03:34:38.635Z", "last_confirmed_current_at": "2026-10-21T08:37:00.433Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-10-21T08:37:00.433Z", "live_updated_at": "2026-10-21T08:37:16.301Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-10-21T08:37:00.433Z", "site_stale_count": 5 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 5, "site_stale_capability_count": 5, "evidence_attested_at": "2026-10-21T03:34:38.635Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.0.4", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-21T03:34:38.635Z", "generated_at": "2026-10-21T03:34:38.635Z", "rendered_at": "2026-10-21T08:37:16.660Z", "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": 7, "total": 7, "failed": 0 }, "invalid": { "passed": 3, "total": 3, "failed": 0 }, "property": { "passed": 3, "total": 3, "failed": 0 }, "round_trip": { "passed": 0, "total": 0, "failed": 0 }, "metamorphic": { "passed": 1, "total": 1, "failed": 0 }, "contract": { "passed": 6, "total": 6, "failed": 0 }, "cross_interface": { "passed": 1, "total": 1, "failed": 0 }, "cross_calculator": { "passed": 5, "total": 5, "failed": 0 } }, "numerical": { "representation": "exact_integer", "tolerance": { "type": "exact", "value": 0, "declared_before_evaluation": true, "rationale": "LCM is an exact integer. Acceptance is exact decimal-string identity vs an O2 module that dual-checks pairwise |a/GCF×b| (own Euclidean GCD) against prime-power LCM when fully factorable. Comparison is exact_equality; ULP is not applicable. Node/V8 is a runtime dependency, not the numeric model. Declared a priori." }, "profile": "exact_integer", "arithmetic": "BigInt", "comparison": "exact_equality", "criterion": "actual exact decimal string === independent oracle exact decimal string", "exact_policy": true, "ulp_applicable": false, "exact_mismatches": 0 }, "coverage": { "partitions": [ { "id": "lcm", "description": "LCM compute", "exercised": true, "case_count": 30 }, { "id": "zero", "description": "Zero in the input set", "exercised": true, "case_count": 5 }, { "id": "negative", "description": "Negative inputs (absolute-value convention)", "exercised": true, "case_count": 3 }, { "id": "beyond-safe-integer", "description": "Magnitude beyond Number.MAX_SAFE_INTEGER", "exercised": true, "case_count": 4 }, { "id": "multi-input-fold", "description": "Fold of three or more inputs", "exercised": true, "case_count": 4 }, { "id": "method-unavailable", "description": "Listing/prime/factor cross-check not available", "exercised": true, "case_count": 4 }, { "id": "xcal", "description": "Cross-calculator vs GCF: GCF(a,b)·LCM(a,b)=|ab| for nonzero integers", "exercised": true, "case_count": 5 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 3 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Least common multiple (pairwise fold)" }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module lcm oracle — independent BigInt pairwise |a/GCF×b| dual-checked against prime-power LCM when factorable (own Euclidean GCD; same runtime as IUT; not IUT transcription)", "engine": { "name": "lcm-reference", "numeric_model": "exact_integer", "criterion": "actual exact decimal string === independent oracle exact decimal string", "independent_of_iut": true, "same_runtime_as_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O2 module backs exact decimal-string identity vs IUT — exact_equality, ULP not applicable", "engine": { "name": "lcm-reference", "numeric_model": "exact_integer", "criterion": "actual exact decimal string === independent oracle exact decimal string", "independent_of_iut": true, "same_runtime_as_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.lcm/1.0.4.json", "evidence_page": "https://www.calculatorx.com/evidence/math.lcm/1.0.4", "calculator": "https://www.calculatorx.com/calc/math/lcm", "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.lcm/1.0.4.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.lcm/1.0.4/2026-10-21.lcm-complete-contract-v2.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.lcm/1.0.4/2026-10-21.lcm-complete-contract-v2.f87d285d6b3e.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }