Categorical dynamics on stable module categories

Lucy Yang

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves hcat(tw)=0 and gives hpol bounds exactly as stated in Theorem 1.2.3, via the ‘pyramid/tower under A’ method and a linear-algebraic lower bound, with all key steps laid out (Theorem 4.2.3; Proposition 4.3.1; Corollary 4.3.2; Theorem 4.3.9) . The candidate solution reproduces the same conclusions but sketches a different route for the upper bound on hcat, invoking a central R-action and ‘Koszul-type’ towers; this technique is not the one used in the paper. A minor technical gap in the candidate solution is the claim that k itself is a compact generator; the paper instead uses a finite direct sum of twists of k as the generator (Proposition 3.5.11) . This does not affect the final conclusions (which agree with the paper) once the generator is chosen as in the paper.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript cleanly establishes vanishing of categorical entropy and sharp-when-available bounds on polynomial entropy for twists in stable module categories of finite connected graded cocommutative Hopf algebras. The use of ‘pyramids’ derived from towers under A is technically apt and well-explained, and the linear-algebraic lower bound is applied appropriately. Minor edits to emphasize the chosen generator and to briefly contrast with other methods would improve clarity and broader accessibility.