Public evidence

math.numerical.derivative

Machine-checked verification for calculation version 1.1.2 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.1.2 · engine_tested · 14/14 tests. It is not the current published claim. Current evidence is 1.1.4 (14/14 tests) · latest.

CVP status

FD of poly/sin/exp, plus method=limit. Discovery /two-sided-limit. Not symbolic d/dx, not one-sided, not L’Hôpital.

Declared partition coverage: PASS · 7/7 declared partitions (tiny-step, subnormal-exp, central, forward, backward, limit, invalid-domain)
Versions: Calculation 1.1.2 · CVP protocol 1.0.0-proposed · Evidence 2026-10-07.derivative-elementary-stability
Verification revision: 2026-10-07.derivative-elementary-stability · 1/1 property · digest 27f3f8a25a41

Verification

Legacy regression suite: 14/14 calculation tests · Production surface contract 4/4

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.

STALE · Build schema 1.1.4 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.derivative-elementary-stability. Calculation version 1.1.2. CVP 1.0.0-proposed. 28/28 golden · 2/2 CVP boundary · 8/8 invalid · 1/1 property · 11/11 cross-interface · 1/1 cross-calculator · 4/4 CVP contract. digest 27f3f8a25a41.

Golden (oracle-backed) 28 / 28
CVP boundary 2 / 2
Invalid input 8 / 8
Property 1 / 1
Cross-interface 11 / 11
Cross-calculator 1 / 1
CVP contract 4 / 4
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.
Verified scope all published methods
Assurance Core

release artifacts aligned PASS
schema output required declared PASS
schema rejects incomplete input PASS
rest success payload validates schema PASS

Fingerprint sha256:dd73311df2b6e31cc00bf131927ce9ba20344f1f597a61c360d3739de4f219e2

Input schema sha256:26040aaa592d3154ca216c017b3ec03ca1e3340e9a03c0e8e8e6ac2593b60a05 · Output schema sha256:d9d7d84992ee8d9667cc38dfba13bfc7d4f32be89a5f53deb878ba4957b28b4b · 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.

Build & scope

Engine identity and declared limitations.

Tool: numerical-derivative
Engine: numerical-derivative
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-17T06:06:06.037Z
Last reviewed: —

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). Same fnValue 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

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

ISO 80000-2:2019 Quantities and units — Mathematics
Supports: Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.
CRC Standard Mathematical Tables — forward, backward, and central differences
Supports: Forward (f(x+h)−f(x))/h; backward; central (f(x+h)−f(x−h))/(2h); two-sided probe of f
NIST DLMF §3.4 — Differentiation — §3.4
Supports: Numerical differentiation using differences, including truncation and rounding considerations.
Gilbert Strang, Calculus — Chapter 2: Derivatives (MIT OpenCourseWare) — §§2.6–2.7 Limits and Continuous Functions
Supports: Two-sided and one-sided limits, continuity, and functions whose limits do not exist. Finite numerical samples alone are not proof of a mathematical limit; CalculatorX’s sampling limitations are stated separately. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.