# Symplectic capacity packing research calculator

Family 343: Symplectic ball packing in higher dimensions. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Symplectic researchers can screen finitely many ball capacities using the stated volume and pairwise capacity inequalities in dimensions at least six.

## Applicability and commercial boundary

Symplectic balls and capacities are not Euclidean storage balls or ordinary packing dimensions. An embedding existence criterion gives no physical layout or constructive numerical embedding.

## Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

## Next verification action

Implement exact inequality checks only for a genuine symplectic workflow and inspect the construction cost.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Symplectic Ball Packings in Higher Dimensions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Symplectic-Ball-Packings-in-Higher-Dimensions-September-23-2026/paper.pdf).