math.transform.z

Three distinct suites: educational examples on the calculator page, this legacy regression count (10/10 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.

This calculator CURRENT · Public schema 1.0.5 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-19.z-input-contract-review. Calculation version 1.0.5. CVP 1.0.0-proposed. 656/656 golden · 2/2 CVP boundary · 22/22 invalid · 1/1 property · 26/26 cross-interface · 5/5 CVP contract. digest d640971981ed.

• Golden (oracle-backed) 656 / 656
• CVP boundary 2 / 2
• Invalid input 22 / 22
• Property 1 / 1
• Cross-interface 26 / 26
• CVP contract 5 / 5
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 8/8 (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. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity.
• Verified scope all published modes
• Assurance Core

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• rest success payload validates schema PASS

Fingerprint sha256:be350c6e5294e38606b4543367a8414cd5dcbda201bd0d888fdbb5898863e707

Input schema sha256:ebd54d7d106e805d80e71d4c780d0400240bde37381cdd525886c1a255b7b054 · Output schema sha256:7407c126a1622690e6057ae9621f4ae9b6f472724961bd5b820cfb94fe30b244 · 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.

Tool

z-transform

Engine

z-transform

Engine build

2026-10-19

Evidence core

2026-10-19T03:14:53.616Z

Rendered

2026-10-23T01:27:11.647Z

Last reviewed

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Assumptions

• Unilateral, causal n≥0
• Real z in the ROC
• Table of named pairs, not a CAS
• The Result Card includes an engine-linked figure of X(z) on the real ROC (pole at |z|=|a|) or a stem of x[n] (at most 16 indices). Same table as REST/MCP.
• Not DFT / FFT
• Not Laplace
• Not residue / two-sided
• Not a pole-zero Argand of complex z

Limitations

• Unilateral causal elementary table; eight named pairs, inverse integer0–64; u[0]=1,a^0=1 including a=0
• Finite real z strictly outside conservative ROC radius on either real branch, including degenerate zero sine; a,z dimensionless, omega radians per sample
• Binary64 approximate evaluation,12 significant digits;2e-11 relative fixture tolerance, no uniform accuracy theorem; conditioned near poles and trig zeros
• Coded decimal input underflow and numerical range/phase/quantization refusals; inverse subnormal relative precision may be refused despite representability
• Aliases must agree; null, nondecimal scalar forms and unknown fields rejected; inverse URL locks mode
• Arbitrary symbolic sequence and contour/residue inversion are outside this named table