math.numerical.definite_integral

Three distinct suites: educational examples on the calculator page, this legacy regression count (13/13 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.

STALE · Build schema 1.1.5 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-07.integral-stability-iface2. Calculation version 1.1.1. CVP 1.0.0-proposed. 83/83 golden · 2/2 CVP boundary · 5/5 invalid · 1/1 property · 3/3 metamorphic · 7/7 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest f22f649f5f61.

• Golden (oracle-backed) 83 / 83
• CVP boundary 2 / 2
• Invalid input 5 / 5
• Property 1 / 1
• Metamorphic 3 / 3
• Cross-interface 7 / 7
• Cross-calculator 1 / 1
• CVP contract 6 / 6
• 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
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:9811d09d5edcaa1e22fd6fe882dffa14e8313312ad202df0a63104b746acafa5

Input schema sha256:03d3c474841c0df54f05cb0de320c8284a768e8dca42efc040237d12ff64c921 · Output schema sha256:27fd356fab3243e5d4e5cfc90bced6473bd6fafb43e221b4483b3f781a4eb616 · 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

definite-integral

Engine

definite-integral

Engine build

2026-10-14

Evidence core

2026-10-14T02:50:33.742Z

Rendered

2026-10-16T14:24:57.490Z

Last reviewed

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Assumptions

• The Result Card includes an engine-linked figure of the integrand on [a, b] (true f shaded; trapezoid/Simpson panel overlays when n≤16; Gauss nodes when method=gauss). Same fnValue as REST/MCP. Not indefinite CAS.
• Polynomial degree ≤ 8
• exact is a binary64 closed-form baseline, not symbolic exact arithmetic. abs_err retains the historical signed value: raw quadrature minus baseline; it is not an error bound.
• Reversed intervals change the sign; equal bounds return zero after input validation.
• Gauss n is nodes 2–8, not panels

Limitations

• Not indefinite / symbolic CAS integrate
• Simpson/trapezoid n panels 2–10000; Simpson n forced even
• Gauss–Legendre n nodes 2–8
• Polynomial degree ≤ 8