Factoring Strongly Irreducible Group Shift Actions onto Full Shifts of Lower Entropy

The uploaded paper proves the factor theorem under the stated hypotheses using subsystem entropy density, a carefully constructed marker block plus tiling (Theorem 4.1), and a quasitiling that factors locally onto an exact tiling via the comparison property (Theorems 2.11–2.13). It then defines a precise sliding block code and proves surjectivity by a controlled pasting inside D-interiors, coding on SD \ D(K ∪ K*) and using an auxiliary map ψ. The candidate solution mirrors this blueprint but makes a critical, self-contradictory choice of a set P with KP ⊂ U while also requiring P ∩ U = ∅ even though e ∈ K, which cannot hold; it also omits the essential K* and ψ components and codes on entire tiles rather than on the protected interior subset. These gaps undermine the correctness of its sliding block code and surjectivity argument.