LIFEGPT: TOPOLOGY-AGNOSTIC GENERATIVE PRETRAINED TRANSFORMER MODEL FOR CELLULAR AUTOMATA

The paper empirically shows that broad-entropy training yields near‑perfect single‑step accuracy on a 32×32 torus, introduces the ARAR procedure, and documents that single‑cell errors can trigger long‑term divergence; these claims are presented as observations rather than formal theorems . The model solution supplies the missing formalism: it (i) corrects the naïve implication that perfect accuracy on a finite dataset forces global correctness by adding the necessary locality/shift‑equivariance assumption, (ii) gives a rigorous ARAR equivalence when f=L, (iii) constructs an explicit permanent‑divergence example, and (iv) provides a coupon‑collector bound showing why broad‑entropy sampling is sufficient to expose all 3×3 neighborhoods with high probability—none of which contradicts the paper; rather, it complements it. The two therefore align in conclusions, reached via different (empirical vs. formal) routes.