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.
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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.
Read original source Pinned manuscript, Theorem 1.1 and Corollary 1.2github.com
Original report: 2026-10-06The 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.
If correct, 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.
A sourced result with the exact hypotheses, baseline, and AI role stated; verification is assessed separately.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
OpenAI reports: a power saving for exact discrete Fourier transforms
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