math.numerical.derivative

Three distinct suites: educational examples on the calculator page, this legacy regression count (14/14 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 1.1.4 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.derivative-input-stencil-contract-v3. Calculation version 1.1.4. CVP 1.0.0-proposed. 255/255 golden · 2/2 CVP boundary · 16/16 invalid · 1/1 property · 16/16 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest 940d2da6a91a.

• Golden (oracle-backed) 255 / 255
• CVP boundary 2 / 2
• Invalid input 16 / 16
• Property 1 / 1
• Cross-interface 16 / 16
• 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 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. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity.
• 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 sha256:79525c25eb284995f558a18329c3d030e763bc3cd00c179170ada37de67a716e

Input schema sha256:6eec6b1f4b1e3bb0de0698ac4697aaead2334559f9ffd4635aa6c62faf271206 · Output schema sha256:d52f8e1bcc9d55c708428d347664c5d17b6ff975a85fb9123ac58b0860529371 · 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

numerical-derivative

Engine

numerical-derivative

Engine build

2026-10-18

Evidence core

2026-10-18T01:58:48.027Z

Rendered

2026-10-23T01:27:11.652Z

Last reviewed

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Assumptions

• The Result Card includes an engine-linked figure of f around x (tangent slope is the published finite difference; two-sided limit draws a horizontal at the probe). Polynomial curve samples use exact dyadic intermediates; sin/exp samples use the same function family as REST/MCP. Not symbolic CAS d/dx.
• Not one-sided limits
• Not L’Hôpital
• Polynomial degree ≤ 8

Limitations

• Not symbolic / CAS d/dx
• Not one-sided left/right; not L’Hôpital
• h ≤ 0 → VALUE_MUST_BE_POSITIVE
• Polynomial degree ≤ 8
• Not a Statistics calculator
• Strict decimal/scalar inputs; nonzero decimal and nonzero primary result underflow reject. Matching aliases required.
• Finite-step value differs from analytic exact; abs_err is signed published value minus published baseline, not a certified bound.
• For polynomial input, x±h denotes exact sums of supplied binary64 values, with exact dyadic intermediates.
• Probe/gap/error diagnostics are rounded binary64 and may quantize to zero; no uniform relative accuracy claim at the subnormal scale.