Ergodic dynamical systems over the Cartesian power of the ring of p-adic integers

The preprint states the correct theorem and outlines a route via the interleaving map H_k and a permutation-induced bijection T_{k,P}, but several core steps are only sketched: (i) T_{k,P} is defined implicitly along D-orbits without a rigorous proof that it is well defined, 1‑Lipschitz, or measure-preserving; (ii) the claimed partition into sets F_k(x0) is asserted with minimal justification; and (iii) the inductive lifting Gn with the needed compatibility is described informally. By contrast, the model gives a complete finite-level construction (via h_n and t_n), proves compatibility, obtains G by inverse limit, and checks measure preservation, transitivity modulo p^k, conjugacy, and ergodicity preservation. In short, the paper’s main claim is right but its proof is incomplete in key places, while the model’s proof is correct and self-contained. See the paper’s theorem and proof outline in Section 3 , the definitions of H_k and T_{k,P} as given by the preprint , the 1‑Lipschitz/compatibility setup in Section 2 , and the subsequent construction and ergodicity discussion .