Local smoothing for the Euclidean wave equation
Source: github.com/openai/math/tree/main/preprints/Local-smoothing-…
OpenAI's October 25 manuscript claims local smoothing in spatial dimension n>=2, with consequences for Kakeya and restriction. The accompanying Lean scope allows arbitrarily small positive Sobolev loss except at p=2 and gives restriction estimates in strict ranges. Released October 26 as raw model output for independent examination; this listing does not assert universal endpoint estimates or independent proof verification.
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— Constantin Kogler (@ConstantinKogl) Oct 26, 2026
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Transformation | Quanta MagazineQuanta Magazine
Proof of the Local Smoothing Conjecture First described by Christopher Sogge in a 1991 paper , the local smoothing conjecture is about how waves like light and sound behave. It posits that as waves spread, they can’t concentrate too much energy in too small of a space for too long of a time. To…