Defects and Frustration in the Packing of Soft Balls

Kenneth Jao, Keith Promislow, Samuel Sottile

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

Part A (single-string equilibria) agrees with the paper’s Proposition 3.1 and uses essentially the same π-rotation symmetry plus uniqueness of the max-center; the O(N^2) counting matches the paper’s bound. Part B: while the model correctly invokes Eisenstein integers and (eventually) reproduces the paper’s formula for A_hex(N), it also makes a contradictory intermediate claim that in the canonical range α depends only on b (α = 1/(√3 b)), independent of a. This contradicts both the paper’s Proposition 3.2 and its worked example (e.g., N=36). Hence the paper’s argument is correct; the model’s contains a substantive error.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper convincingly establishes the equilibria structure of single-string tessellations and gives a precise and constructive characterization of rectangular N-hex tori via Eisenstein integers. The numerical sections are thorough and well-motivated. Minor polishing would further improve readability and reproducibility.