This update to OpenAI Problem #130 introduces an all-length bound of T(n) = O(n(log n)^(1−δ)) with δ = 0.0007547360. This figure is 10.34 times higher than the exponent saving of Shea's previous δ = 7.3×10⁻⁵ and builds on frameworks by Jacob Sussman and constructions by Chafik Boukhalfa. The result utilizes OpenAI's exact-complex-arithmetic model as a theoretical benchmark and does not claim any increase in practical FFT speed.
Wednesday, October 21, 2026
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Lean Verifies Identities in Ryan Shea's Updated DFT Bound
AI11 days ago
The arithmetic and key finite identities of a proposed algorithm for computing the discrete Fourier transform have been validated through a formal proof process. James Chang used the Lean proof assistant to perform this check, which is designed to identify errors that traditional test examples might miss. Ryan Shea, who developed the research using Codex, clarified that while these finite checks pass, they do not establish the universal theorem, and the work still requires independent review and a novelty assessment.
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