Classification of Backward Filtrations and Factor Filtrations: Examples from Cellular Automata

The paper proves: (i) the factor filtration built from the deterministic automaton τ is not dynamically standard, and (ii) for sufficiently large noise ε, the factor filtration of the PCA τε is dynamically standard. Both claims are established rigorously via dynamical I-cosiness/entropy arguments and an explicit immersion into a product-type noise filtration, respectively. By contrast, the model’s Part (i) incorrectly concludes that the underlying static filtration F^{τ−1} is not standard (the paper shows it is of product type), and its I-cosiness argument conflates static and dynamical notions. Part (ii) of the model gives a plausible alternative (Dobrushin) route to dynamic standardness at high noise, consistent in spirit with the paper but not the method used there.