Public evidence

math.transform.dft

Machine-checked verification for calculation version 1.2.0 · tier engine_tested

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Verification

17/17 calculation tests · Production surface contract 3/3

Golden tests 6 / 6
Boundary tests 3 / 3
Property tests 8 / 8
Production surface contract 3 / 3
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.2.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain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:a8cbd603acbe8623de3e7ad27a3ff568d86892697430cc7ff689c74709856ed6

Input schema sha256:f063080da5b0e18188f2ff460a1ad27239f3f9c5e16a0ce2ab68000d6af9d487 · Output schema sha256:032879b320a62a7f2d82d7119a81a838343abbbd576270aa73bb0d06c83fa050 · 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: discrete-fourier-transform
Engine: discrete-fourier-transform
Engine build: 2026-09-20
Evidence core: 2026-09-20T07:48:45.138Z
Rendered: 2026-09-20T09:07:29.783Z
Last reviewed: —

Assumptions

Direct O(N²) DFT/IDFT; radix-2 FFT/IFFT
Numpy backward normalization
N ≤ 64; FFT N = 2^k
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

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-dft-impulse`	golden	pass	Expected n=4 · algorithm=direct · normalization=backward · Actual n=4 · mode=dft · algorithm=direct · normalization=backward · formula=X[k] = Σ_n x[n] e^{−2πi kn/N}
`golden-dft-dc`	golden	pass	Expected n=4 · Actual n=4 · mode=dft · algorithm=direct · normalization=backward · formula=X[k] = Σ_n x[n] e^{−2πi kn/N}
`golden-idft-dc`	golden	pass	Expected n=4 · Actual n=4 · mode=idft · algorithm=direct · normalization=backward · formula=x[n] = (1/N) Σ_k X[k] e^{2πi kn/N}
`boundary-dft-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`golden-fft-impulse`	golden	pass	Expected n=4 · algorithm=radix2 · normalization=backward · Actual n=4 · mode=fft · algorithm=radix2 · normalization=backward · formula=X[k] = Σ_n x[n] e^{−2πi kn/N}
`golden-fft-dc`	golden	pass	Expected n=4 · algorithm=radix2 · Actual n=4 · mode=fft · algorithm=radix2 · normalization=backward · formula=X[k] = Σ_n x[n] e^{−2πi kn/N}
`golden-ifft-dc`	golden	pass	Expected n=4 · algorithm=radix2 · Actual n=4 · mode=ifft · algorithm=radix2 · normalization=backward · formula=x[n] = (1/N) Σ_k X[k] e^{2πi kn/N}
`boundary-fft-n3`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-dft-n65`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`property-dft-impulse`	property	pass	impulse → ones
`property-dft-dc`	property	pass	DC → N at bin 0
`property-idft-dc`	property	pass	IDFT DC → ones
`property-dft-roundtrip`	property	pass	IDFT(DFT(impulse))
`property-fft-impulse`	property	pass	FFT impulse → ones
`property-fft-dc`	property	pass	FFT DC → N at bin 0
`property-fft-matches-dft`	property	pass	FFT = DFT for N=8
`property-fft-roundtrip`	property	pass	IFFT(FFT(impulse))