OpenAI · 130-01 · 2026-09-25 · Theoretical computer science
An explicit power saving for the exact discrete Fourier transform
preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026
Family 130. Fourier transforms below .
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Gives a deterministic length- discrete Fourier transform algorithm using operations for every , with explicit . The model uses exact complex arithmetic, unrestricted coefficients and a supplied root of unity, and counts scalar preparation and logarithmic-word indexing.
We give a deterministic algorithm that computes the discrete Fourier transform at every length n in 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.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 130: Exact Fourier transforms below . The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.