OpenAI and Anthropic both announced on October 26, 2026, that internal large language models independently discovered algorithms refuting the Exponential Time Hypothesis (ETH) for 3-SAT and #k-SAT, achieving subexponential 2^{o(n)} runtime with polynomial space via techniques like sparse polynomial reductions and Lean formalization. The public GitHub preprints, dated to an October 16 discovery, have drawn immediate expert attention, including a review group led by ETH originators Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams. Simplified follow-up proofs from researchers like Ryan O'Donnell have emerged, while the lack of full peer review and the labs' competitive releases create uncertainty around final acceptance. Traders are watching the working group's conference and any formal rebuttals for resolution signals.
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