Remark: Family 079. Sogge's local smoothing conjecture in dimension three

Resolves Sogge's local smoothing conjecture for the Euclidean wave equation in three spatial dimensions. The estimate holds throughout the full strict range $2<p<\infty$, with Sobolev regularity above $\max \{0,1-3/p\}$. In particular, the critical $L^3$ estimate holds with every positive Sobolev loss.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.