Symplectic Ball Packings in Higher Dimensions

We prove that, for all integers n ≥ 3 and k ≥ 1 and all positive real capacities $R_1,\dots ,R_k$, the closed standard symplectic $2n$-balls of these capacities embed disjointly into the interior of a ball of capacity R > 0 if and only if $\sum _{i=1}^k{R}_i^n<R^n,R_i+R_j<R(i\ne j).$ Capacity is π times the squared Euclidean radius, and each embedding is defined on a neighborhood of its closed source ball. This proves Siegel and Yao's Conjecture A.