OpenAI math repo adds new Lean-verified papers, including an ETH refutation claim
danintheory · x · 2026-10-27
danintheory shares updates to the openai/math repository's history.md. Two new manuscripts with Lean formalizations were added October 26:
- Local smoothing for the Euclidean wave equation: proves Sogge's local smoothing in every spatial dimension ≥2 via an auxiliary PDE, also yielding the Kakeya maximal/dimension conjectures and Stein's spherical restriction estimates; raw model output released
- The Exponential Time Hypothesis is False: a deterministic algorithm exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space; the 3-SAT case refutes ETH. An independent working group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will examine the proof
This follows the earlier announcement of Lean-verified QCD and Yang–Mills existence proofs. Withdrawn papers document their gaps in READMEs.
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