Improving OpenAI's bound on the exact discrete Fourier transform below n log n

A research draft published on OpenAI Problem #130 proposes an all-length bound of T(n) = O(n(log n)^(1−δ)) with δ = 7.3×10⁻⁵ for computing the exact discrete Fourier transform, a 730-million-fold increase in the exponent saving over OpenAI's published δ = 10⁻¹³. The draft builds on Swapnil Jain's round-six complex network for Problem #109 and its cited predecessors, transferring those advances from integer multiplication to the Fourier setting. A sixth update to OpenAI Problem #109 reports κ > 2⁻¹⁵, tightened from κ = 2⁻¹⁸², with an exact witness of 3.667 × 10⁻⁵, about 2.4-fold over the previous 1.548 × 10⁻⁵ and a 2¹⁶⁷-fold improvement over the original OpenAI result.