{ "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": "plane-geometry", "version": "1.5.1", "title": "Plane Geometry Calculator", "formula_family": "plane-geometry", "capability_id": "math.geometry.plane", "verification_revision": "2026-10-28.metric-scope-v3" }, "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": "22.20.0", "numeric_model": "IEEE-754 binary64", "os": "darwin" }, "suite": { "id": "plane-geometry", "version": "1.5.1", "uri": "https://www.calculatorx.com/evidence/math.geometry.plane/1.5.1.json", "verification_revision": "2026-10-28.metric-scope-v3" }, "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-XCAL-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "ISO 80000-2:2019 Quantities and units — Mathematics", "kind": "standard", "reference": "Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.", "url": "https://www.iso.org/standard/64973.html" }, { "label": "CRC Standard Mathematical Tables — plane polygons", "kind": "other", "reference": "Regular n-gon A = (n s²)/(4 tan(π/n)); parallelogram A = ab sin θ; shoelace / Meister–Gauss polygon area" }, { "label": "Euclid’s Elements — I.35: Parallelograms on the Same Base", "kind": "other", "reference": "Equal-base, equal-height parallelograms have equal area. Comparing with a rectangle gives A = base × perpendicular height; side length is not generally the height. Mathematical reference only; not validation or endorsement of this implementation.", "url": "https://mathcs.clarku.edu/~djoyce/elements/bookI/propI35.html" }, { "label": "Gilbert Strang, Calculus — Chapter 9: Polar Coordinates and Complex Numbers (MIT OpenCourseWare)", "kind": "other", "reference": "§§9.1–9.3 Polar Coordinates, Length and Area", "url": "https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch09.pdf" }, { "label": "Gilbert Strang, Calculus — Chapter 15: Vector Calculus (MIT OpenCourseWare)", "kind": "other", "reference": "§15.3 Green’s Theorem", "url": "https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch15.pdf" }, { "label": "Gilbert Strang, Calculus — Chapter 1: Introduction to Calculus (MIT OpenCourseWare)", "kind": "other", "reference": "§1.5 A Review of Trigonometry", "url": "https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch01.pdf" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "Rectangle, square, regular n-gon, annulus, parallelogram, isosceles trapezoid, irregular polygon (shoelace)." }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Seven Euclidean plane shapes; strict bounded decimals, normal binary64 positive measures, exact dyadic polygon area/topology, stable ring and angle formulas; complete secondary outputs. Simple3–8 vertex polygons and safe-integer regular n; no CAS." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "Consistent length; A in length², P in length" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O2 expected_values + O2 numerical_behavior" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "9/9 legacy golden; 155/155 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "4/4 numeric-edge Evidence + 1/1 near-singularity numeric; illegal enum/system is Invalid only" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "5 Evidence illegal-input + 50/50 oracle-backed error-code (exact_error_match, not ULP)" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "diagnostic_raw_leaf_ulp_max (not an acceptance budget)=3; policy declared a priori" }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "8/8 declared partitions (rectangle, square, regular-polygon, annulus, parallelogram, trapezoid, irregular-polygon, invalid-domain) · 9 legacy golden / 5 CVP boundary unique cases · 5 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 plane-geometry; 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 @ 2026-10-29T01:22:37.788Z · live site-wide report stale @ 2026-10-29T01:23:59.828Z (52 other capabilities) · local checks pass · attestation_id=52c69c777f14b3653d6a0d99fffe81ea840d401226015698a80d3880c8382ade · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-29T01:22:37.788Z · Live production status STALE (52 capabilities; 324 remain CURRENT) @ 2026-10-29T01:23:59.828Z · Public schema 1.5.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.5.1 · 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=0904162d9842ae579e660eb678ec02f2ca6e852dd03b716905c0a6501acd7dae · verified_at=2026-10-28T16:33:53.880Z · evidence_attested_at=2026-10-28T16:33:53.880Z · last_confirmed_current_at=2026-10-29T01:22:37.788Z · rendered_at=2026-10-29T01:24:00.066Z · binds=cvp_core_sha256", "check_result": "PASS", "production_state": "CURRENT", "binding_current": true }, "CVP-DIM-01": { "result": "PASS", "applicability": "applicable", "notes": "Euclidean plane" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "4/4 property · enumerated fixed assertions (not generated; no seed)" }, "CVP-META-01": { "result": "PASS", "applicability": "applicable", "notes": "2/2 metamorphic; domain=1; input-contract=1; limited to assessed relations/preconditions" }, "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-rect-pythagorean PASS vs math.pythagorean; xcal-annulus-circles PASS vs math.geometry.circle" }, "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": "47913aaa9464e88c81ea7f637b61c1d3e3b1361c311e4131082c464d1765f9f9", "evidence_digest": "0c354d2744d91d0efcd81adf4fd89300f487ee665e7a9b07a43816a13c30a550", "production_sha256": "0904162d9842ae579e660eb678ec02f2ca6e852dd03b716905c0a6501acd7dae", "attested_catalog_sha256": "163b0d7072a58bed20a0320572211167e1629730bef43c185b5f545ceac7744c", "production_checks": [ { "id": "math.geometry.plane:output-const", "status": "pass", "detail": "output const 1.5.1 vs capability 1.5.1", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" }, { "id": "math.geometry.plane:evidence-sha256", "status": "pass", "detail": "6d787585f372", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" }, { "id": "math.geometry.plane:semantic-contract", "status": "pass", "detail": "25/25", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" }, { "id": "math.geometry.plane:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.5.1 vs origin 1.5.1", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" }, { "id": "math.geometry.plane:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.geometry.plane/1.5.1/2026-10-28.metric-scope-v3/core/0c354d2744d9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z", "projection_compared": false }, { "id": "math.geometry.plane:cvp-latest-alias-agrees", "status": "pass", "detail": "math.geometry.plane/1.5.1/2026-10-28.metric-scope-v3/core/0c354d2744d9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z", "projection_compared": false }, { "id": "math.geometry.plane:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" }, { "id": "math.geometry.plane:cvp-immutable-manifest-sha256", "status": "pass", "detail": "0c354d2744d9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" }, { "id": "math.geometry.plane:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.geometry.plane/1.5.1/2026-10-28.metric-scope-v3/core/0c354d2744d9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z", "projection_compared": false }, { "id": "math.geometry.plane:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" }, { "id": "math.geometry.plane:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-28T16:33:53.880Z" } ], "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": "0c354d2744d91d0efcd81adf4fd89300f487ee665e7a9b07a43816a13c30a550", "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": "0c354d2744d91d0efcd81adf4fd89300f487ee665e7a9b07a43816a13c30a550", "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": "6d787585f3726a1bb616fb7fc8bdf24a59485af90ba21c69fff37fc378ce127b", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "163b0d7072a58bed20a0320572211167e1629730bef43c185b5f545ceac7744c", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "0c354d2744d91d0efcd81adf4fd89300f487ee665e7a9b07a43816a13c30a550" }, "dependencies": [ { "name": "plane-geometry-engine", "version": "1.5.1" }, { "name": "plane-geometry-reference-oracle", "version": "1.0.0" }, { "name": "math.pythagorean", "version": "1.1.6", "role": "cross_calculator_peer", "capability_id": "math.pythagorean", "evidence_digest": "4e661f033102d57e25604c76c92b099170b889cd33df23f00e2c46ec22307d0c", "evidence": "https://www.calculatorx.com/evidence/math.pythagorean/1.1.6.cvp.json" }, { "name": "math.geometry.circle", "version": "1.1.2", "role": "cross_calculator_peer", "capability_id": "math.geometry.circle", "evidence_digest": "5d1d32fed335b23a9da1a913d4371429add16ecd3faa24e34b56fa7f07ad2d90", "evidence": "https://www.calculatorx.com/evidence/math.geometry.circle/1.1.2.cvp.json" }, { "name": "node", "version": "22.20.0" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "52c69c777f14b3653d6a0d99fffe81ea840d401226015698a80d3880c8382ade", "attested_at": "2026-10-28T16:33:53.880Z", "last_confirmed_current_at": "2026-10-29T01:22:37.788Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-10-29T01:22:37.788Z", "live_updated_at": "2026-10-29T01:23:59.828Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-10-29T01:22:37.788Z", "site_stale_count": 52 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 52, "site_stale_capability_count": 52, "evidence_attested_at": "2026-10-28T16:33:53.880Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.5.1", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-28T16:33:53.880Z", "generated_at": "2026-10-28T16:33:53.880Z", "rendered_at": "2026-10-29T01:24:00.066Z", "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": 155, "total": 155, "failed": 0 }, "boundary": { "passed": 5, "total": 5, "failed": 0 }, "invalid": { "passed": 55, "total": 55, "failed": 0, "comparison": "exact_error_match" }, "property": { "passed": 4, "total": 4, "failed": 0, "kind": "fixed" }, "round_trip": { "passed": 0, "total": 0, "failed": 0 }, "metamorphic": { "passed": 2, "total": 2, "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": "Normalized binary64; exact dyadic predicates/polynomial intermediates, binary64 trigonometry, finite normal positive outputs", "tolerance": { "type": "relative", "value": 1e-11, "rationale": "Independent mpmath750; exact branch/count/array cardinality and strict numeric types; no raw-input perturbation bound.", "declared_before_evaluation": true }, "max_error_observed": 3, "error_metric": "diagnostic_raw_leaf_ulp", "comparison_evidence_protocol": "scoped-comparison-v1", "max_error_observed_scope": "Raw finite matching numeric leaves across records/hops; diagnostic only. Acceptance is the per-record/hop comparison predicate and its declared scoped policy." }, "coverage": { "partitions": [ { "id": "rectangle", "description": "rectangle", "exercised": true, "case_count": 35 }, { "id": "square", "description": "square", "exercised": true, "case_count": 15 }, { "id": "regular-polygon", "description": "regular_polygon", "exercised": true, "case_count": 26 }, { "id": "annulus", "description": "annulus", "exercised": true, "case_count": 16 }, { "id": "parallelogram", "description": "parallelogram", "exercised": true, "case_count": 45 }, { "id": "trapezoid", "description": "trapezoid", "exercised": true, "case_count": 18 }, { "id": "irregular-polygon", "description": "irregular_polygon", "exercised": true, "case_count": 29 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 55 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Euclidean plane area and perimeter identities" }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Python mpmath750 Euclidean identities / exact-rational polygon fan reference", "engine": {} }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Independent high-precision small/large/thin-ring/angle/polygon reference and complete-output comparator negative controls", "engine": {} } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.geometry.plane/1.5.1.json", "evidence_page": "https://www.calculatorx.com/evidence/math.geometry.plane/1.5.1", "calculator": "https://www.calculatorx.com/calc/math/plane-geometry", "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.geometry.plane/1.5.1.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.geometry.plane/1.5.1/2026-10-28.metric-scope-v3.cvp.json", "manifest_core": "https://www.calculatorx.com/evidence/math.geometry.plane/1.5.1/2026-10-28.metric-scope-v3.0c354d2744d9.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }