Public evidence

math.transform.laplace

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

10/10 calculation tests · Production surface contract 3/3

Golden tests 3 / 3
Boundary tests 2 / 2
Property tests 5 / 5
Production surface contract 3 / 3
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain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 valid input executes PASS
engine success output validates schema PASS

Fingerprint sha256:75e50b1948e5f958df0509387b65eb3f392d9e5806bf4b358978469eabd7f50a

Input schema sha256:16caca56512f8a5de48c149ac283b719fba6af4ec75e4b51201d8d91109939ff · Output schema sha256:a7515f430ae98a7c258b2896985c7756be1ce8df62a95a040b628cab896b5cf3 · 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: laplace-transform
Engine: laplace-transform
Engine build: 2026-09-20
Evidence core: 2026-09-20T04:08:31.012Z
Rendered: 2026-09-20T09:07:29.783Z
Last reviewed: —

Assumptions

Unilateral, causal t≥0
Real s in the ROC
Table of named pairs, not a CAS
Not DFT / FFT
Not Z-transform
Not Bromwich / two-sided

Limitations

Unilateral causal table only
Real s in the ROC; t ≥ 0
Not DFT / FFT
Not Z-transform — later canonical
Not Bromwich / two-sided / CAS
unknown mode (including dft, z, cas) → INVALID_MODE

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-laplace-exp`	golden	pass	Expected value=0.5 · algorithm=table · Actual n=0 · value=0.5 · mode=laplace · f=exp · a=-1 · omega=1 · algorithm=table · roc=Re(s)>-1
`golden-laplace-step`	golden	pass	Expected value=1 · Actual n=0 · value=1 · mode=laplace · f=step · a=0 · omega=1 · algorithm=table · roc=Re(s)>0
`golden-ilaplace-exp`	golden	pass	Expected value=1 · Actual n=0 · value=1 · mode=inverse · f=exp · a=-1 · omega=1 · algorithm=table · roc=Re(s)>-1
`boundary-laplace-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-laplace-roc`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`property-laplace-exp`	property	pass	L{e^{−t}}(1)=1/2
`property-laplace-step`	property	pass	L{1}(1)=1
`property-laplace-sin`	property	pass	L{sin t}(1)=1/2
`property-ilaplace-exp0`	property	pass	e^{−t} at 0
`property-ilaplace-ramp`	property	pass	ramp t=3