{ "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": "quadratic", "version": "1.1.1", "title": "Quadratic Formula Calculator", "formula_family": "quadratic", "capability_id": "math.quadratic", "verification_revision": "2026-10-13.quadratic-interface-replay" }, "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": "20.19.2", "numeric_model": "IEEE-754 binary64", "os": "darwin" }, "suite": { "id": "quadratic", "version": "1.1.1", "uri": "https://www.calculatorx.com/evidence/math.quadratic/1.1.1.json", "verification_revision": "2026-10-13.quadratic-interface-replay" }, "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-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "Margaret Stevens — The Maths Workbook (University of Oxford)", "kind": "other", "reference": "Chapter 1, §3.4: Quadratic Equations", "url": "https://www.some.ox.ac.uk/wp-content/uploads/2024/08/Maths-Workbook.pdf" }, { "label": "Gilbert Strang, Calculus — Chapter 9: Polar Coordinates and Complex Numbers (MIT OpenCourseWare)", "kind": "other", "reference": "§9.4 Complex Numbers", "url": "https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch09.pdf" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "x = (−b ± √Δ)/(2a), evaluated with cancellation-safe q-form" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Declared partitions are two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain — plus inequality-two-roots, inequality-repeated, inequality-no-real-roots, inequality-rhs, inequality-fractions; not a claim that every quadratic is covered. Near-double-root, large-scale, and cancellation are numerical-boundary partitions and are in the O3 tabulated ULP claim." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless" }, "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": "6/6 legacy golden; 40/40 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 Evidence illegal-input + 7/7 oracle-backed error-code (exact_error_match, not ULP)" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, tiny-complex, tiny-real, tiny-scale, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a)." }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "14/14 declared partitions (inequality-two-roots, inequality-repeated, inequality-no-real-roots, inequality-rhs, inequality-fractions, two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain) · 6 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 quadratic; 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 @ 2026-10-14T16:06:21.473Z · live site-wide report stale @ 2026-10-14T16:06:24.009Z (3 other capabilities) · local checks pass · attestation_id=3e91f5ef575c2270f9ec6c2d3a81023a6fd63f3a226ffb5185b1499537e66272 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-14T16:06:21.473Z · Live production status STALE (3 capabilities; 373 remain CURRENT) @ 2026-10-14T16:06:24.009Z · Public schema 1.1.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.1.1 · 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 · cvp-reproduce-manifest-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=717df72e5aa7ed1160816959e2b61c083741151c248a1caa9cd9447b4b054376 · verified_at=2026-10-13T09:47:37.551Z · evidence_attested_at=2026-10-13T09:47:37.551Z · last_confirmed_current_at=2026-10-14T16:06:21.473Z · rendered_at=2026-10-14T16:06:24.362Z · 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": "5/5 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": "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). ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 3/3 (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. Core profile does not include Live-graph integration. Label collision, near-double-root markers, viewport switching, and pointer interaction need independent visual tests." }, "CVP-ORACLE-01": { "result": "PASS", "applicability": "higher_assurance", "notes": "O3 12/12 tabulated vectors vs IUT · ≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, tiny-complex, tiny-real, tiny-scale, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a)." }, "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 3/3 (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. Core profile does not include Live-graph integration. Label collision, near-double-root markers, viewport switching, and pointer interaction need independent visual tests." }, "artifacts": { "evidence_bundle_sha256": "94d20131b613b2b2f1e36b31b56d2c3bf752611692dfdb95d62598a8792e55e0", "evidence_digest": "4dddb83bf6dfe4c331af410041afc2ff39693f25144d76ebdd4fb485cf657ed3", "production_sha256": "717df72e5aa7ed1160816959e2b61c083741151c248a1caa9cd9447b4b054376", "attested_catalog_sha256": "2ec8209bd773c3b6a186bdb8439e3adac379d819ff51de11e92ac166fc9d1e36", "production_checks": [ { "id": "math.quadratic:output-const", "status": "pass", "detail": "output const 1.1.1 vs capability 1.1.1", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:evidence-sha256", "status": "pass", "detail": "b6e1ffc3ffd6", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:semantic-contract", "status": "pass", "detail": "9/9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.1.1 vs origin 1.1.1", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.quadratic/1.1.1/2026-10-13.quadratic-interface-replay/core/4dddb83bf6df", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z", "projection_compared": false }, { "id": "math.quadratic:cvp-latest-alias-agrees", "status": "pass", "detail": "math.quadratic/1.1.1/2026-10-13.quadratic-interface-replay/core/4dddb83bf6df", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z", "projection_compared": false }, { "id": "math.quadratic:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:cvp-immutable-manifest-sha256", "status": "pass", "detail": "4dddb83bf6df", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.quadratic/1.1.1/2026-10-13.quadratic-interface-replay/core/4dddb83bf6df", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z", "projection_compared": false }, { "id": "math.quadratic:cvp-reproduce-manifest-agree", "status": "pass", "detail": "2026-10-13.quadratic-interface-replay · 6c8e67f2ed03", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" }, { "id": "math.quadratic:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-13T09:47:37.551Z" } ], "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": "4dddb83bf6dfe4c331af410041afc2ff39693f25144d76ebdd4fb485cf657ed3", "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": "4dddb83bf6dfe4c331af410041afc2ff39693f25144d76ebdd4fb485cf657ed3", "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": "b6e1ffc3ffd641bd77a97ec36327f79e2852bfcf3993a2a80f435897da3a53b9", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "2ec8209bd773c3b6a186bdb8439e3adac379d819ff51de11e92ac166fc9d1e36", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "4dddb83bf6dfe4c331af410041afc2ff39693f25144d76ebdd4fb485cf657ed3" }, "dependencies": [ { "name": "quadratic-engine", "version": "1.1.1" }, { "name": "quadratic-reference-oracle", "version": "1.0.0" }, { "name": "quadratic-mpmath-o3-table", "version": "quadratic-mpmath-o3" }, { "name": "node", "version": "20.19.2" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "3e91f5ef575c2270f9ec6c2d3a81023a6fd63f3a226ffb5185b1499537e66272", "attested_at": "2026-10-13T09:47:37.551Z", "last_confirmed_current_at": "2026-10-14T16:06:21.473Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-10-14T16:06:21.473Z", "live_updated_at": "2026-10-14T16:06:24.009Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-10-14T16:06:21.473Z", "site_stale_count": 3 }, "live_site_status": { "href": "/.well-known/calculatorx-production-attestation.json" }, "bound_snapshot_site_stale_count": 3, "site_stale_capability_count": 3, "evidence_attested_at": "2026-10-13T09:47:37.551Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.1.1", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-13T09:47:37.551Z", "generated_at": "2026-10-13T09:47:37.551Z", "rendered_at": "2026-10-14T16:06:24.362Z", "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": 40, "total": 40, "failed": 0 }, "boundary": { "passed": 3, "total": 3, "failed": 0 }, "invalid": { "passed": 10, "total": 10, "failed": 0, "comparison": "exact_error_match" }, "property": { "passed": 5, "total": 5, "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": 11, "total": 11, "failed": 0 }, "o3": { "passed": 12, "total": 12, "failed": 0, "claim_scope": "≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, tiny-complex, tiny-real, tiny-scale, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a).", "max_error_ulp": 0.67108864, "table_sha256": "6c8e67f2ed03b75a193e76be0cfa73781cd43587d0004503148223de0a9cbb8c" } }, "numerical": { "representation": "IEEE-754 binary64 quadratic formula", "tolerance": { "type": "ulp", "value": 4, "rationale": "Independent Δ/roots vs IUT; ≤4 ULP on primary roots/delta. Declared a priori. O3 tabulated vectors (including cancellation and large-scale) use the same threshold.", "declared_before_evaluation": true }, "max_error_observed": 0.67108864, "claim_scope": "≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, tiny-complex, tiny-real, tiny-scale, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a)." }, "coverage": { "partitions": [ { "id": "inequality-two-roots", "description": "Independent interval oracle: two-roots", "exercised": true, "case_count": 9 }, { "id": "inequality-repeated", "description": "Independent interval oracle: repeated", "exercised": true, "case_count": 8 }, { "id": "inequality-no-real-roots", "description": "Independent interval oracle: no-real-roots", "exercised": true, "case_count": 9 }, { "id": "inequality-rhs", "description": "Independent interval oracle: rhs", "exercised": true, "case_count": 1 }, { "id": "inequality-fractions", "description": "Independent interval oracle: fractions", "exercised": true, "case_count": 1 }, { "id": "two-real", "description": "Δ > 0 two distinct real roots", "exercised": true, "case_count": 6 }, { "id": "repeated", "description": "Δ = 0 repeated real root", "exercised": true, "case_count": 11 }, { "id": "complex", "description": "Δ < 0 complex conjugate roots", "exercised": true, "case_count": 5 }, { "id": "irrational", "description": "Δ > 0 not a perfect square", "exercised": true, "case_count": 3 }, { "id": "near-double-root", "description": "Numerical boundary: Δ ≈ 0 close real roots", "exercised": true, "case_count": 5 }, { "id": "large-scale", "description": "Numerical boundary: widely separated real roots (O3 tabulated ULP)", "exercised": true, "case_count": 2 }, { "id": "fraction-input", "description": "Fractional coefficients (parser + roots)", "exercised": true, "case_count": 3 }, { "id": "cancellation", "description": "Numerical boundary: b² ≫ 4ac (O3 tabulated ULP; cancellation-safe q-form)", "exercised": true, "case_count": 6 }, { "id": "invalid-domain", "description": "a = 0 or missing coefficients", "exercised": true, "case_count": 10 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Quadratic formula and discriminant" }, { "class": "O3", "reference_scope": "expected_values", "scope": "expected_values", "label": "Precomputed mpmath/MPFR quadratic formula (80 dps) rounded to nearest binary64 — not Node Math.sqrt", "engine": { "name": "quadratic-mpmath-o3", "library": "mpmath 1.4.1", "mpmath_dps": 80, "precision_bits": 265, "independent_of_iut": true, "generator_version": "1.2.0", "generator_sha256": "5a1157ecb5e8c163ca72f377c162c8501077f46d22cc32eba7a80a0855a83a36", "table_sha256": "6c8e67f2ed03b75a193e76be0cfa73781cd43587d0004503148223de0a9cbb8c" } }, { "class": "O3", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O3 table vs IUT Δ/roots; ≤4 ULP on tabulated vectors only, not the whole coefficient space", "engine": { "name": "quadratic-mpmath-o3", "library": "mpmath 1.4.1", "mpmath_dps": 80, "precision_bits": 265, "independent_of_iut": true, "generator_version": "1.2.0", "generator_sha256": "5a1157ecb5e8c163ca72f377c162c8501077f46d22cc32eba7a80a0855a83a36", "table_sha256": "6c8e67f2ed03b75a193e76be0cfa73781cd43587d0004503148223de0a9cbb8c" } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Independent completed-square sign-chart interval oracle", "engine": { "name": "quadratic-inequality-reference", "precision_bits": 53, "independent_of_iut": true } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module quadratic oracle — independent formula", "engine": { "name": "quadratic-reference", "precision_bits": 53, "independent_of_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O2 module backs ≤4 ULP root/delta comparison vs IUT", "engine": { "name": "quadratic-reference", "precision_bits": 53, "independent_of_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.quadratic/1.1.1.json", "evidence_page": "https://www.calculatorx.com/evidence/math.quadratic/1.1.1", "calculator": "https://www.calculatorx.com/calc/math/quadratic", "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.quadratic/1.1.1.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.quadratic/1.1.1/2026-10-13.quadratic-interface-replay.cvp.json", "reproduce": "https://www.calculatorx.com/evidence/math.quadratic/reproduce", "manifest_core": "https://www.calculatorx.com/evidence/math.quadratic/1.1.1/2026-10-13.quadratic-interface-replay.4dddb83bf6df.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }