Symplectic ball packing in higher dimensions

Resolves the Siegel–Yao conjecture for arbitrary capacities in every dimension $2n\ge6$. Finitely many closed symplectic balls of capacities $R_1,\ldots,R_k$ embed disjointly into an open ball of capacity R exactly when $\sum_iR_i^n\lt R^n$ and $R_i+R_j\lt R$ for every distinct pair i, j.