Real and complex analysis·OpenAI Math·Result 079
Local smoothing in three dimensions
One of the 372 results in OpenAI's public mathematics catalogue, filed under real and complex analysis: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Critical local smoothing for the three-dimensional wave equation
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What OpenAI claims
Resolves Sogge's local smoothing conjecture for the Euclidean wave equation in three spatial dimensions. The estimate holds throughout the full strict range 2 < p < ∞, with Sobolev regularity above max {0,1-3/p}. In particular, the critical L3 estimate holds with every positive Sobolev loss.
Paper
Critical local smoothing for the three-dimensional wave equation
We prove the critical L3 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.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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