Remark: Family 343. Sharp symplectic ball-packing criteria in higher dimensions

Resolves the Siegel–Yao conjecture for arbitrary capacities in every dimension $2n\ge 6$. Finitely many closed symplectic balls of capacities $R_1,\dots ,R_k$ embed disjointly into an open ball of capacity $R$ exactly when ${\sum }_i{R}_i^n<R^n$ and $R_i+R_j<R$ for every distinct pair $i,j$.

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.