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OpenAI reports: a power saving for exact discrete Fourier transforms

The manuscript reports one deterministic algorithm computing the exact complex discrete Fourier transform at every length n in O(n(log n)^(1−10^−13)) operations, including scalar preparation, scheduling and indexing, in its specified arithmetic model.

Sources for this record

What was already known

Classical arbitrary-length FFT methods use O(n log n) arithmetic operations. Prior constant-factor improvements and restricted-model lower bounds do not settle the unrestricted-coefficient model used here.

What changed and why it matters

Breaks the n log n arithmetic-operation scale for all transform lengths in the stated model; the small saving and practical limitations do not erase its theoretical impact.

The AI contribution

OpenAI attributes the manuscript to an internal frontier model. Exact human contributions to the individual argument are not established by release-wide attribution.

Limitations

Unit-cost exact complex arithmetic, unrestricted coefficient magnitudes, O(log n)-bit indexing and one specified Fourier root are assumed. This is not a bit-complexity or numerical-stability theorem and does not contradict bounded-coefficient or well-conditioned lower bounds. The tiny exponent saving gives no practical-speedup guarantee. AIProofWatch has not audited the proof.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The source reports this precise contribution; statement review does not establish a proof audit.

Accessible artifact / proof

Accessible supporting proof or code; not compiled or reproduced by AIProofWatch.

Correction and publication history

2026-10-11 · publication

Public-discussion audit found this substantive scoped contribution missing. Source statement, baseline, attribution and importance reviewed; no full proof audit. Historical addition without subscriber alerts.

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