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
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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