{"id":"openai-math/Critical-local-smoothing-for-the-three-dimensional-wave-equation","pdf":"https://github.com/openai/math/blob/main/preprints/Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026","tags":["harmonic-analysis","wave-equation","local-smoothing"],"score":0,"title":"Critical local smoothing for the three-dimensional wave equation","domain":"Real and complex analysis","family":"079","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We prove the critical L 3 local smoothing estimate for the wave equation in three spatial dimensions, with every positive Sobolev loss. This resolves Sogge's Euclidean local smoothing conjecture in dimension three.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.12681","date":"2026-10-08","kind":"web","site":"arXiv.org","text":"We obtain the $L^3$ reverse square function estimate for the light cone in four dimensions from the critical local-smoothing and round-cone propagation statements in the September 2026 OpenAI manuscript. We state these inputs, together with the plate maximal theorem of Di Plinio and Parissis, in a…","added":"2026-10-24","title":"The square function estimate for the cone in four dimensions","author":"Faruk Temur","record":"arxiv/2610.12681"}],"formalized":false,"family_title":"Local smoothing for the Euclidean wave equation","formalizations":["https://github.com/openai/math/blob/main/lean/docs/079.md"]}