Public evidence

math.numerical.derivative

Machine-checked verification for calculation version 1.1.0 · tier engine_tested

Open calculator API Capability Download JSON MCP Review policy

Verification

14/14 calculation tests · Production surface contract 2/2

Golden tests 4 / 4
Boundary tests 3 / 3
Property tests 7 / 7
Production surface contract 2 / 2
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.1.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract PASS
Evidence attested at 2026-09-18T21:41:55.460Z
Last production check 2026-09-18T21:41:55.460Z
Public / cache —
Origin —
Supplemental domain review Not performed
Named expert review Not performed

release artifacts aligned PASS
schema rejects incomplete input PASS

Fingerprint sha256:cfb3188e47cf6d62c7892ce78f2e6fae4fe8a2b5c9180a421d51854ca3ec6080

Input schema sha256:b0fdc50254fe780d196197c5286273de7e183056af7cbcb0d81dd14321eb1a54 · Output schema sha256:74c2da2136b9e89e6fb0579aef8ca04a8c8b199418aabf2454ab24af5106d414 · 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: 2026-09-19
Evidence core: 2026-09-19T13:47:01.267Z
Rendered: 2026-09-20T09:07:29.786Z
Last reviewed: —

Assumptions

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

Published checks

Golden, boundary, and property cases included in this evidence build.

ID	Kind	Status	Detail
`golden-x2`	golden	pass	Expected exact=6 · Actual value=6.00000000084 · method=central · integrand=poly · x=3 · h=0.000001 · exact=6 · abs_err=8.38667801872e-10 · formula=(f(x+h) − f(x−h)) / (2h)
`golden-sin0`	golden	pass	Expected exact=1 · Actual value=1 · method=central · integrand=sin · x=0 · h=0.000001 · exact=1 · abs_err=-1.66644475996e-13 · formula=(f(x+h) − f(x−h)) / (2h)
`golden-limit-x2`	golden	pass	Expected exact=9 · method=limit · Actual value=9 · method=limit · integrand=poly · x=3 · h=0.000001 · exact=9 · abs_err=1.00008890058e-12 · formula=[f(x+h) + f(x−h)] / 2
`golden-limit-sin0`	golden	pass	Expected exact=0 · quantity=limit · Actual value=0 · method=limit · integrand=sin · x=0 · h=0.000001 · exact=0 · abs_err=0 · formula=[f(x+h) + f(x−h)] / 2
`boundary-h-zero`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-autodiff`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-onesided`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`property-d-x2`	property	pass	d(x²)/dx at 3
`property-d-x2-fd`	property	pass	central x² ≈ 6
`property-d-x`	property	pass	d(x)/dx
`property-d-sin`	property	pass	cos 0
`property-d-exp`	property	pass	e⁰
`property-lim-x2`	property	pass	lim x² at 3
`property-lim-sin`	property	pass	lim sin 0