Public evidence

math.transform.z

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

Open calculator API Capability Download JSON MCP Review policy

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Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain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 sha256:40c2ec119d496c769d43a0f04082c03f0274cd9e243e03a9741da61c706fa932

Input schema sha256:c82b1a7d78bf5d37443f1f7a10933efc674429835a4a4a83eb89bfbbd9cf0686 · Output schema sha256:0dd237c25777fe9149d1c56a446ab6fdefe878474b3b7ab8da4b6f6bbb302a8b · 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: z-transform
Engine: z-transform
Engine build: 2026-09-20
Evidence core: 2026-09-20T04:27:10.707Z
Rendered: 2026-09-20T09:07:29.783Z
Last reviewed: —

Assumptions

Unilateral, causal n≥0
Real z in the ROC
Table of named pairs, not a CAS
Not DFT / FFT
Not Laplace
Not residue / two-sided

Limitations

Unilateral causal table only
Real z in the ROC; integer n ≥ 0
Not DFT / FFT
Not Laplace — separate canonical
Not residue / two-sided / CAS
unknown mode (including dft, laplace, 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-z-geom`	golden	pass	Expected value=2 · algorithm=table · Actual value=2 · mode=z · f=geom · a=0.5 · omega=1 · algorithm=table · roc=\|z\|>0.5 · formula=z/(z−a)
`golden-z-step`	golden	pass	Expected value=2 · Actual value=2 · mode=z · f=step · a=0.5 · omega=1 · algorithm=table · roc=\|z\|>1 · formula=z/(z−1)
`golden-iz-geom`	golden	pass	Expected value=1 · Actual n=0 · value=1 · mode=inverse · f=geom · a=0.5 · omega=1 · algorithm=table · roc=\|z\|>0.5
`boundary-z-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-z-roc`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`property-z-geom`	property	pass	Z{(1/2)^n}(1)=2
`property-z-step`	property	pass	Z{1}(2)=2
`property-z-sin`	property	pass	Z{sin(πn/2)}(2)=2/5
`property-iz-geom0`	property	pass	(1/2)^n at 0
`property-iz-ramp`	property	pass	ramp n=3