{"id":"openai-math/Local-smoothing-for-the-Euclidean-wave-equation","pdf":"https://github.com/openai/math/blob/main/preprints/Local-smoothing-for-the-Euclidean-wave-equation-October-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Local-smoothing-for-the-Euclidean-wave-equation-October-25-2026","score":0,"title":"Local smoothing for the Euclidean wave equation","domain":"Real and complex analysis","family":"079","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":3,"published":"2026-10-25","reactions":{},"discussion":[{"url":"https://www.quantamagazine.org/update/168483/#:~:text=Proof%20of%20the%20Local%20Smoothing%20Conjecture%20First%20described%20by%20Christopher%20Sogge","kind":"web","site":"Quanta Magazine","text":"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…","added":"2026-11-03","title":"Transformation | Quanta Magazine"},{"url":"https://x.com/ConstantinKogl/status/2114838472066515342","date":"2026-10-26","kind":"x","added":"2026-11-03","author":"Constantin Kogler","handle":"ConstantinKogl"},{"url":"https://x.com/JamesLeng15/status/2114875830228906072","date":"2026-10-27","kind":"x","added":"2026-11-03","author":"James Leng","handle":"JamesLeng15"}],"formalized":true,"family_title":"Local smoothing for the Euclidean wave equation","formalizations":["https://github.com/openai/math/blob/main/lean/docs/079.md"]}