OpenAI AI-generated manuscript claims proof of local smoothing conjecture in all dimensions
jiqizhixin · x · 2026-11-08
OpenAI has released an AI-generated manuscript (dated October 2025) claiming a proof of local smoothing for the Euclidean wave equation in every spatial dimension of at least two.
- Core difficulty: sharp estimates must control how wave concentrations propagate, linking the problem to the geometry of Kakeya sets containing line segments in every direction.
- Mechanism: the manuscript introduces auxiliary flows and associated energy estimates to establish the smoothing inequalities, and derives a full Hausdorff dimension conclusion for Kakeya sets.
- Significance: if the argument withstands independent scrutiny, it would settle major conjectures in harmonic analysis. The claim is public and undergoing independent verification, with a Lean formalization effort underway.
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