Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 343-01. Symplectic Ball Packings in Higher Dimensions
Manuscript map · lines 8995–9004
OpenAI@2026-10-07#rem:oai-p-343-01
Authors: OpenAI. Family 343.
Title: Symplectic Ball Packings in Higher Dimensions.
Abstract: We prove that, for all integers n ≥ 3 and k ≥ 1 and all positive real capacities $R_1,{}ldots,R_k$, 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 ${}displaystyle {}sum_{i=1}{}k R_i{}n{}lt R{}n, {}qquad R_i+R_j{}lt R{}quad(i{}ne j).$ 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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