Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 130-01. An explicit power saving for the exact discrete Fourier transform
Manuscript map · lines 4925–4934
OpenAI@2026-10-07#rem:oai-p-130-01
Authors: OpenAI. Family 130.
Title: An explicit power saving for the exact discrete Fourier transform.
Abstract: We give a deterministic algorithm that computes the discrete Fourier transform at every length n in $O(n({}log n){}{1-10{}{-13}})$ operations. The model uses exact complex arithmetic, unrestricted coefficients, specified Fourier roots, and unit-cost logarithmic-size indexing; scalar preparation and array organization are included.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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