The proof was verified using a pinned Lean build and incorporates exact certificates and a contribution audit. The research builds on earlier advances in integer multiplication from OpenAI Problem #109, specifically complex network developments by Swapnil Jain, and vastly exceeds OpenAI's original bound of δ = 10⁻¹³. Separately, an open source project called sfFFT has demonstrated 3.8x to 6.1x end-to-end speedups on DGX Spark GB10 hardware for lengths up to 8192, although it reports higher error rates than the cuFFT implementation.
Wednesday, October 21, 2026
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Ryan Shea Boosts OpenAI Problem 130 DFT Bound by 10.34x
Tech11 days ago
A revised algorithm for computing the discrete Fourier transform (DFT) further lowers the theoretical number of operations required for the process. Ryan Shea published an update to OpenAI Problem #130 proposing an all length bound of T(n) = O(n(log n)^(1−δ)) with δ = 0.0007547360, a 10.34 times increase in the exponent saving over his previous announcement of δ = 7.3×10⁻⁵. The stronger result incorporates a five-stage framework from Jacob Sussman and constructions by Chafik Boukhalfa. Shea stated that no practical FFT speedup is claimed from this result, which uses OpenAI's exact-complex-arithmetic model.
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