Research Draft Claims DFT Computable Below n log n with 730-Million-Fold Exponent Gain
basedjensen · x · 2026-10-09
Sub-n log n Discrete Fourier Transform Proposed for OpenAI Problem #130
- A research draft by Ryan Shea proposes computing the exact DFT below n log n.
- It proposes an all-length bound T(n) = O(n(log n)^(1−δ)) with δ = 7.3×10⁻⁵ — a 730-million-fold increase in exponent saving over OpenAI's published δ = 10⁻¹³.
- The approach builds on Swapnil Jain's round-six complex network for Problem #109, transferring advances from integer multiplication to the Fourier setting. It's a draft, not a peer-reviewed result.
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