ON ASYNCHRONOUS NON-UNIFORM CELLULAR AUTOMATA AND SOFIC GROUPS

The paper proves that over finitely generated sofic groups, every stably injective ANUCA is invertible (Theorem A), via a sofic-approximation counting argument and a uniform invertibility result (Theorem 8.1) . The model’s claimed counterexample misreads the paper’s Example 16.1, which is injective but not stably injective and hence does not refute Theorem A; indeed σ_q is non-injective and q ∈ Σ(s), so σ_s is not stably injective . For Part (C), the model’s conclusion matches the paper: post-surjective ANUCA on finitely generated sofic groups are pre-injective and invertible (Theorem 13.1 + Theorem 12.3, with Corollary 4.5 giving surjectivity) .