2406.06195
2D MOORE CA WITH NEW BOUNDARY CONDITIONS AND ITS REVERSIBILITY
B.A. OMIROV, SH.B. REDJEPOV, J.B. USMONOV
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Lemma 5.1 and Theorem 5.3 establish exactly the same rank decomposition and reversibility criterion that the candidate derives, both under the hypothesis that the constant superdiagonal block X (here B1) is invertible. Both arguments use block Gaussian elimination/Schur-complement steps on X and produce the same Pk recursion and the formula rank(T) = (m−1)n + rank(Pm); the model’s exposition differs only in presentation (two-sided elimination to a block-diagonal form) but is mathematically equivalent to the paper’s row-operation proof.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The central lemma and its application are correct and well aligned with established block Gaussian elimination techniques. The paper’s framing in the Moore CA setting with mixed boundaries is well motivated, and the reversibility test is practically useful. Minor clarifications (notation alignment, brief discussion of alternative elimination orders) would improve readability but do not affect correctness.