math.transform.dft

Three distinct suites: educational examples on the calculator page, this legacy regression count (17/17 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.

STALE · Build schema 1.2.3 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-09.dft-complete-json-mobile. Calculation version 1.2.1. CVP 1.0.0-proposed. 13/13 golden · 3/3 CVP boundary · 10/10 invalid · 1/1 property · 7/7 cross-interface · 5/5 CVP contract. digest 803f88691f89.

• Golden (oracle-backed) 13 / 13
• CVP boundary 3 / 3
• Invalid input 10 / 10
• Property 1 / 1
• Cross-interface 7 / 7
• 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 2/2 (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.
• 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 sha256:20f0d60096365c9b227c73d836f6214280a8585c466037848802e12348b17662

Input schema sha256:4eeaae0c876db5ffa281e82bc50fea4ef145b7c25f01269ba711e13d76553d72 · Output schema sha256:a046adcc1206295f1ff1734ecec799ad03556afa7813155c46e77cb3133d2ca9 · 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

discrete-fourier-transform

Engine

discrete-fourier-transform

Engine build

2026-10-14

Evidence core

2026-10-14T02:50:33.742Z

Rendered

2026-10-18T12:52:03.505Z

Last reviewed

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Assumptions

• Direct O(N²) DFT/IDFT; radix-2 FFT/IFFT
• Numpy backward normalization
• N ≤ 64; FFT N = 2^k
• The Result Card includes an engine-linked stem figure of |X[k]| (forward) or |x[n]| (inverse); marker is index 0. Same mag as REST/MCP.
• Not Laplace / Z
• Not CAS

Limitations

• Direct O(N²) DFT/IDFT, N≤64; radix-2 FFT/IFFT, N=2^k ≤64
• Numpy backward: unnormalized forward, 1/N inverse
• FFT agrees with DFT for power-of-2 N (Float64)
• Not Laplace / Z — other canonicals
• Not CAS
• unknown mode (including laplace, cas) → INVALID_MODE