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.

This calculator CURRENT · Public schema 1.2.3 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.dft-input-dyadic-surface-v2. Calculation version 1.2.3. CVP 1.0.0-proposed. 145/145 golden · 3/3 CVP boundary · 14/14 invalid · 1/1 property · 7/7 cross-interface · 6/6 CVP contract. digest f373e71ceba5.

• Golden (oracle-backed) 145 / 145
• CVP boundary 3 / 3
• Invalid input 14 / 14
• Property 1 / 1
• Cross-interface 7 / 7
• CVP contract 6 / 6
• 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
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:22d5188e8df7111ed82c621d7a2736f7b9be7a1a6e0485737ef11563f254d7a7

Input schema sha256:1553739d52167044cbb764f9d3f7fcc9d21cc3dc6da3d0694a640ec86faa9d96 · Output schema sha256:84bd236e11b9d1bd0e5b7f1deba6dcc77e8de6f4d9f0045598e1fb6ff8f716e1 · 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

2026-10-19

Evidence core

2026-10-19T01:35:20.040Z

Rendered

2026-10-22T08:54:35.173Z

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
• Decimal nonzero input underflow → NUMERIC_UNDERFLOW; malformed/conflicting inputs rejected.
• Exact dyadic sums/products of binary64 twiddles; no exact transcendental or per-bin relative guarantee near cancellation zeros.
• Nonzero evaluated output component below binary64 or nonfinite output/magnitude → NUMERICAL_RANGE_ERROR. Intermediate overflow is avoided. Input echoes retain binary64; outputs publish12 significant digits.