math.numerical.ode

Three distinct suites: educational examples on the calculator page, this legacy regression count (9/9 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.1.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-18.ode-input-polynomial-surface-v3. Calculation version 1.1.1. CVP 1.0.0-proposed. 141/141 golden · 2/2 CVP boundary · 17/17 invalid · 1/1 property · 12/12 O3 · 8/8 cross-interface · 1/1 cross-calculator · 5/5 CVP contract. digest f6deeacd0aae. Relative 1e-8 comparison of y and exact against listed fixed-step references; not a whole-domain accuracy guarantee or a user-tolerance acceptance.

• Golden (oracle-backed) 141 / 141
• CVP boundary 2 / 2
• Invalid input 17 / 17
• Property 1 / 1
• O3 high-precision 12 / 12
• Cross-interface 8 / 8
• Cross-calculator 1 / 1
• CVP contract 5 / 5
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim 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.
• Verified scope all published methods
• Assurance Core

• 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

Fingerprint sha256:561c36f3d0381a72bbd6f3e64fcc2ed76606765e189a55b5a1329fa99a328f31

Input schema sha256:76f7d15fb6093a1cfca27199d6571322d789a599ac7012371c89573ef2159f22 · Output schema sha256:89d59e3d5b954d05402cc590fd56c6aedbe6f972553fd3a9441d862632f62cf1 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

ordinary-differential-equation

Engine

ordinary-differential-equation

Engine build

2026-10-18

Evidence core

2026-10-18T12:51:28.122Z

Rendered

2026-10-23T01:27:11.653Z

Last reviewed

—

Assumptions

• The Result Card includes an engine-linked Live graph of numerical y(t) using the same Overview / Focus template as Log (Overview window t0…t1; current point is published y(t1); same Euler/RK4 stepper as REST/MCP). Exact y(t1) is a reference when it differs. Not rk45, not systems, not PDE, not CAS.
• Scalar first-order only
• Polynomial quadrature and baseline use exact dyadic intermediates over binary64 inputs and actual representable time nodes; output remains binary64, not symbolic.
• y, exact and signed difference publish12 significant digits; model inputs and h retain binary64 precision. The graph is sampled to at most257 points, not a complete trajectory export.
• Polynomial degree ≤ 8

Limitations

• Not rk45 / adaptive / Dormand–Prince
• Not systems of ODEs or second-order IVP
• Not PDE / CAS / symbolic solve
• n ≤ 10000
• t1 = t0 → INVALID_INPUT
• n must be an integer; fractional steps and unknown inputs are rejected
• abs_err is a legacy signed difference before publication rounding; diagnostics names signed/absolute/relative error explicitly
• Fixed-step method completion is not accuracy acceptance; inspect diagnostics and warnings
• Finite decimal text only; aliases must agree; explicit empty modes/fields do not default.
• Polynomial intermediates and quadrature sums use exact binary64-input dyadic arithmetic; final results are binary64 projections.
• Raw input/model fields and h retain binary64 precision; y, exact and error publish12 significant digits. Live graph uses at most257 samples and is not a complete trajectory export.