A natural class of cellular automata containing fractional multiplication automata, Rule 30, and others

The paper’s Theorem 3.5 proves that no width-w spatial trace of a number-like configuration can be eventually periodic for a rapidly left expansive CA, using Lemma 3.2 to propagate periodicity leftward and then a spreading-speed argument to contradict s < 1/h. The model reproduces the leftward propagation idea but (i) inserts an unproven width constraint h + d ≤ w − 1 and proposes an invalid ‘increase w’ remedy, and (ii) its ‘staircase’ step incorrectly concludes s(F) ≥ 1/h from invariance on a left half-line—this invariance would, if anything, block leftward motion rather than force it. The paper’s argument is coherent and matches the stated definitions and lemmas, whereas the model’s proof contains key logical gaps and a sign error in the speed conclusion. See Definition 3.1, Definition 3.3, Definition 3.4, Lemma 3.2, and the proof of Theorem 3.5 in the paper .