Public evidence

math.numerical.definite_integral

Machine-checked verification for calculation version 1.1.0 · tier engine_tested

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Verification

13/13 calculation tests · Production surface contract 4/4

Golden tests 5 / 5
Boundary tests 2 / 2
Property tests 6 / 6
Production surface contract 4 / 4
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: STALE · Last attested schema matched 1.1.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-19T00:00:17.039Z
Semantic contract PASS
Evidence attested at 2026-09-18T21:41:55.460Z
Last production check 2026-09-18T21:41:55.460Z
Public / cache PASS
Origin PASS
Supplemental domain review Not performed
Named expert review Not performed

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS

Fingerprint sha256:66f15a967f127accc2dcbb7e1f95893afc51db14e3c65844cd0d837faab244e0

Input schema sha256:61855b6a58b7725c9c0a355c4ce3caa90fc53bc7b8dbd4d87c5934308d008821 · Output schema sha256:1730192812118fe6d77f189cbd938ca9cfb811fd6ee349f8eea1583080a4d040 · 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: definite-integral
Engine: definite-integral
Engine build: 2026-09-19
Evidence core: 2026-09-19T01:35:56.101Z
Rendered: 2026-09-19T02:14:29.320Z
Last reviewed: —

Assumptions

Not indefinite CAS
Polynomial degree ≤ 8
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

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-x-dx`	golden	pass	Expected exact=0.5 · Actual n=10 · value=0.5 · method=simpson · integrand=poly · a=0 · b=1 · exact=0.5 · abs_err=0
`golden-x2`	golden	pass	Expected value=0.3333333333333333 · exact=0.3333333333333333 · Actual n=10 · value=0.333333333333 · method=simpson · integrand=poly · a=0 · b=1 · exact=0.333333333333 · abs_err=0
`golden-sin-pi`	golden	pass	Expected exact=2 · Actual n=200 · value=2.00000000068 · method=simpson · integrand=sin · a=0 · b=3.141592653589793 · exact=2 · abs_err=6.76473099759e-10
`golden-gauss-x`	golden	pass	Expected value=0.5 · exact=0.5 · Actual n=2 · value=0.5 · method=gauss · integrand=poly · a=0 · b=1 · exact=0.5 · abs_err=0
`golden-gauss-x2`	golden	pass	Expected value=0.3333333333333333 · exact=0.3333333333333333 · Actual n=2 · value=0.333333333333 · method=gauss · integrand=poly · a=0 · b=1 · exact=0.333333333333 · abs_err=0
`boundary-gauss-n`	boundary	pass	Expected VALUE_ABOVE_MAX · Actual VALUE_ABOVE_MAX
`boundary-romberg`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`property-int-x`	property	pass	∫x
`property-int-x2`	property	pass	∫x² Simpson
`property-int-sin`	property	pass	∫sin
`property-int-exp`	property	pass	∫e^x
`property-int-trap`	property	pass	∫₀² x
`property-int-gauss-x2`	property	pass	∫x² Gauss