2011.14191
Endomorphisms of Linear Shifts of Finite Type
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves the five-way equivalence (a)–(e) for linear cellular automata on topologically mixing linear subshifts over finitely generated infinite groups (Theorem 1.9), including (b)⇒(a) via a Baire category argument and (e)⇒(a) using the separate nilpotency⇔{0}-limit-set theorem (Theorem 1.8). The candidate solution establishes the same equivalences, but its (b)⇒(a) step uses a pattern-packing/gluing construction plus finite-speed propagation. Under the hypotheses stated, the candidate’s approach is sound, while differing from the paper’s method. Hence both are correct with different proofs.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper’s statements and proofs are correct and complete for the stated hypotheses, and the candidate solution reaches the same equivalences, providing a valid alternative proof of the key (b)⇒(a) step using a packing argument. Minor additions clarifying the gluing lemma derivation from mixing would improve the candidate write-up. Overall, both contributions are solid and mutually reinforcing.