Geometry and topology · Oct 6, 2026

Symplectic ball packing in higher dimensions

Resolves the Siegel–Yao conjecture for arbitrary capacities in every dimension 2n≥62n\ge6. Finitely many closed symplectic balls of capacities R1,…,RkR_1,\ldots,R_k embed disjointly into an open ball of capacity R exactly when ∑iRin<Rn\sum_iR_i^n\lt R^n and Ri+Rj<RR_i+R_j\lt R for every distinct pair i, j.

Contributors

Unreleased OpenAI model

AI systems: Unreleased OpenAI model

Sources