{ "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": "ordinary-differential-equation", "version": "1.1.1", "title": "Ordinary Differential Equation Calculator", "formula_family": "ode", "capability_id": "math.numerical.ode", "verification_revision": "2026-10-18.ode-input-polynomial-surface-v3" }, "profile": "core", "verified_scope": "all published methods", "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": "ordinary-differential-equation", "version": "1.1.1", "uri": "https://www.calculatorx.com/evidence/math.numerical.ode/1.1.1.json", "verification_revision": "2026-10-18.ode-input-polynomial-surface-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-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 — Euler and classical RK4", "kind": "other", "reference": "Forward Euler y ← y+h f; classical RK4 four-stage step; exact y0 e^{kΔt} for y′=ky" }, { "label": "Gilbert Strang, Calculus — 16.2 Differential Equations", "kind": "other", "reference": "Section 16.2, Numerical Methods (PDF page 13)", "url": "https://ocw.mit.edu/ans7870/textbooks/Strang/Edited/Calculus/16.1-16.2.pdf" } ] }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "Independent discrete linear amplification, scaled analytic exponential and rational polynomial reference vs 12-digit publication" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Scalar first-order IVP. Discovery /euler-method and /runge-kutta lock method. Not rk45, not systems, not PDE, not CAS." }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O2 expected_values + O3 expected_values + O2 numerical_behavior" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "3/3 legacy golden; 141/141 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "1/1 numeric-edge Evidence + 1/1 near-singularity numeric; illegal enum/system is Invalid only" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "2 Evidence illegal-input + 15/15 oracle-backed error-code (exact_error_match, not ULP)" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "Relative comparison of published y and exact against discrete/closed-form references at the a-priori 1e-8 threshold; zero references require exact zero. ULP is not the acceptance metric, and this is not user-tolerance acceptance of the IVP solution." }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "7/7 declared partitions (exponential-range, shifted-time, scaled-results, numerical-range, euler, rk4, invalid-domain) · 3 legacy golden / 2 CVP boundary unique cases · 2 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 ordinary-differential-equation; 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 @ 2026-10-19T07:58:46.038Z · live site-wide report stale @ 2026-10-19T07:58:58.938Z (5 other capabilities) · local checks pass · attestation_id=c64cc612dc6c3a945c8f29b84029807be91aeb07eee35eea41b94b1b8594e211 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-19T07:58:46.038Z · Live production status STALE (5 capabilities; 371 remain CURRENT) @ 2026-10-19T07:58:58.938Z · 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=589b90803730d03fdb921029dbc9e570b3d8a9047e839174126db3b72f2cd1c6 · verified_at=2026-10-18T12:52:51.057Z · evidence_attested_at=2026-10-18T12:52:51.057Z · last_confirmed_current_at=2026-10-19T07:58:46.038Z · rendered_at=2026-10-19T07:58:59.390Z · binds=cvp_core_sha256", "check_result": "PASS", "production_state": "CURRENT", "binding_current": true }, "CVP-DIM-01": { "result": "PASS", "applicability": "applicable", "notes": "scalar IVP" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "1/1 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": "1/1 cross-calculator · xcal-const-integral PASS vs math.numerical.definite_integral" }, "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 2/2 (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": "PASS", "applicability": "higher_assurance", "notes": "O3 12/12 tabulated vectors vs IUT · Relative 1e-8 comparison of y and exact against listed fixed-step references; not a whole-domain accuracy guarantee or a user-tolerance acceptance." }, "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 2/2 (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": "6ff5de69b6960290ce23324f962a268260cd826eccf2ce3512a031e5f9033a55", "evidence_digest": "f6deeacd0aae79230335db0cb65d809c95ffc78da90d80389b6397216a5ae16f", "production_sha256": "589b90803730d03fdb921029dbc9e570b3d8a9047e839174126db3b72f2cd1c6", "attested_catalog_sha256": "93b711f8b5b8d602c9f2ecfb852b561e5cd33585603555116fdf45f0bd4f1957", "production_checks": [ { "id": "math.numerical.ode: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": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode:evidence-sha256", "status": "pass", "detail": "77444970d9ea", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode:semantic-contract", "status": "pass", "detail": "9/9", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode: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": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.numerical.ode/1.1.1/2026-10-18.ode-input-polynomial-surface-v3/core/f6deeacd0aae", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z", "projection_compared": false }, { "id": "math.numerical.ode:cvp-latest-alias-agrees", "status": "pass", "detail": "math.numerical.ode/1.1.1/2026-10-18.ode-input-polynomial-surface-v3/core/f6deeacd0aae", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z", "projection_compared": false }, { "id": "math.numerical.ode:cvp-immutable-manifest-fetch", "status": "pass", "detail": "public=200 origin=200", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode:cvp-immutable-manifest-sha256", "status": "pass", "detail": "f6deeacd0aae", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode:cvp-latest-alias-matches-immutable", "status": "pass", "detail": "math.numerical.ode/1.1.1/2026-10-18.ode-input-polynomial-surface-v3/core/f6deeacd0aae", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z", "projection_compared": false }, { "id": "math.numerical.ode:cvp-reproduce-manifest-agree", "status": "pass", "detail": "2026-10-18.ode-input-polynomial-surface-v3 · 518a0b0215be", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode:calculator-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z" }, { "id": "math.numerical.ode:evidence-html-cvp-projection", "status": "pass", "detail": "matches Trust display", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-10-18T12:52:51.057Z" } ], "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": "f6deeacd0aae79230335db0cb65d809c95ffc78da90d80389b6397216a5ae16f", "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": "f6deeacd0aae79230335db0cb65d809c95ffc78da90d80389b6397216a5ae16f", "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": "77444970d9ea60b81b72346b7ea9ca5fa1e8f0ecd0c9f2c779eb37c0f6698dfd", "note": "Published Evidence JSON core — Trust freshness / production bind subject" }, { "name": "evidence_catalog_digest", "field": "artifacts.attested_catalog_sha256", "digest_scope": "capability_catalog", "value": "93b711f8b5b8d602c9f2ecfb852b561e5cd33585603555116fdf45f0bd4f1957", "note": "Capability catalog integrity; site-wide, not per-suite fingerprint" } ] }, "cvp_core_sha256": "f6deeacd0aae79230335db0cb65d809c95ffc78da90d80389b6397216a5ae16f" }, "dependencies": [ { "name": "ordinary-differential-equation-engine", "version": "1.1.1" }, { "name": "ordinary-differential-equation-reference-oracle", "version": "1.0.0" }, { "name": "ode-exact-input-decimal-table", "version": "ode-machine-decimal-1" }, { "name": "math.numerical.definite_integral", "version": "1.1.5", "role": "cross_calculator_peer", "capability_id": "math.numerical.definite_integral", "evidence_digest": "535933d707a31981fee7139ff19a128e898259d3a35bff0a1b9b989145ea203c", "evidence": "https://www.calculatorx.com/evidence/math.numerical.definite_integral/1.1.5.cvp.json" }, { "name": "node", "version": "22.20.0" } ], "attestation": { "status": "CURRENT", "href": "/.well-known/calculatorx-production-attestation.json", "id": "c64cc612dc6c3a945c8f29b84029807be91aeb07eee35eea41b94b1b8594e211", "attested_at": "2026-10-18T12:52:51.057Z", "last_confirmed_current_at": "2026-10-19T07:58:46.038Z", "site_attestation_current": false, "capability_attestation_current": true, "bound_snapshot_status": "pass", "live_report_status": "stale", "bound_attested_at": "2026-10-19T07:58:46.038Z", "live_updated_at": "2026-10-19T07:58:58.938Z", "bound_snapshot": { "status": "pass", "attested_at": "2026-10-19T07:58:46.038Z", "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": "2026-10-18T12:52:51.057Z" }, "domain_review": { "status": "ABSENT", "spec_version": "1.1.1", "external_third_party": false, "note": "Named expert review not performed" }, "timestamps": { "verified_at": "2026-10-18T12:52:51.057Z", "generated_at": "2026-10-18T12:52:51.057Z", "rendered_at": "2026-10-19T07:58:59.390Z", "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": 141, "total": 141, "failed": 0 }, "boundary": { "passed": 2, "total": 2, "failed": 0 }, "invalid": { "passed": 17, "total": 17, "failed": 0, "comparison": "exact_error_match" }, "property": { "passed": 1, "total": 1, "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": 8, "total": 8, "failed": 0 }, "cross_calculator": { "passed": 1, "total": 1, "failed": 0 }, "o3": { "passed": 12, "total": 12, "failed": 0, "claim_scope": "Relative 1e-8 comparison of y and exact against listed fixed-step references; not a whole-domain accuracy guarantee or a user-tolerance acceptance.", "table_sha256": "518a0b0215be576e12777419116829e4c2b6349c4b0a6448afabee04032e5103" } }, "numerical": { "representation": "IEEE-754 binary64; 12 significant digits without nonzero clamping", "tolerance": { "type": "relative", "value": 1e-8, "rationale": "Nonzero reference y and exact require relative 1e-8 for declared golden step counts; Zero references require exact numerical zero, including discrete underflow; subnormal nonzero references retain the relative gate and may fail because of step quantization. Linear y uses the closed fixed-step amplification formula; exact remains the analytic IVP. Polynomial golden step counts are selected for declared accuracy.", "declared_before_evaluation": true }, "max_error_observed": 4.5308846881684436e-12, "claim_scope": "Relative 1e-8 comparison of y and exact against listed fixed-step references; not a whole-domain accuracy guarantee or a user-tolerance acceptance.", "error_metric": "relative" }, "coverage": { "partitions": [ { "id": "exponential-range", "description": "Scaled analytic exponential and fixed-step linear amplification", "exercised": true, "case_count": 7 }, { "id": "shifted-time", "description": "Representable grids at nonzero time origins", "exercised": true, "case_count": 5 }, { "id": "scaled-results", "description": "Nonzero small-scale publication", "exercised": true, "case_count": 2 }, { "id": "numerical-range", "description": "Unrepresentable step or reference", "exercised": true, "case_count": 11 }, { "id": "euler", "description": "euler", "exercised": true, "case_count": 79 }, { "id": "rk4", "description": "rk4", "exercised": true, "case_count": 84 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 17 } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "y′=k y or y′=p(t); forward Euler and classical RK4" }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Listed independent exact-binary64 Fraction composite quadrature and Decimal amplification100/180dps; not a whole-domain guarantee", "engine": { "name": "Python Fraction and Decimal", "precision_bits": 598, "independent_of_iut": true, "same_runtime_as_iut": false, "generator_sha256": "161fb96a58d86475fce4b617aafb8b0f3f4ab600975c1b5c2607904aaa06df95", "table_sha256": "0d524012ea77b837e7aa6ac4c79661340aeb57febce59d3bc806e43bb258f373" } }, { "class": "O3", "reference_scope": "expected_values", "scope": "expected_values", "label": "Exact-binary64-input Python Decimal at 100/160 decimal digits; listed fixtures only", "engine": { "name": "Python decimal", "precision_bits": 332, "independent_of_iut": true, "same_runtime_as_iut": false, "generator_sha256": "6e4a3034f74b373f68423419741cfa8e93728e6320ab4ae897320659ade7ce96", "table_sha256": "518a0b0215be576e12777419116829e4c2b6349c4b0a6448afabee04032e5103" } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module ODE oracle — bounded-power exponential scaling, closed fixed-step amplification and exact rational polynomial antiderivative differences, not IUT Euler/RK4 transcription", "engine": { "name": "numerical-ode-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 discrete linear solution and analytic reference vs IUT stepper + 12-digit publication — nonzero relative 1e-8 and exact numerical zero", "engine": { "name": "numerical-ode-reference", "precision_bits": 53, "independent_of_iut": true, "same_runtime_as_iut": true } } ] }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.numerical.ode/1.1.1.json", "evidence_page": "https://www.calculatorx.com/evidence/math.numerical.ode/1.1.1", "calculator": "https://www.calculatorx.com/calc/math/ordinary-differential-equation", "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.numerical.ode/1.1.1.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.numerical.ode/1.1.1/2026-10-18.ode-input-polynomial-surface-v3.cvp.json", "reproduce": "https://www.calculatorx.com/evidence/math.numerical.ode/reproduce", "manifest_core": "https://www.calculatorx.com/evidence/math.numerical.ode/1.1.1/2026-10-18.ode-input-polynomial-surface-v3.f6deeacd0aae.cvp.json" }, "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }