Multiorders in amenable group actions

The paper’s Theorem 7.4 correctly proves that for any multiorder and for ν-almost every order, the remote past along that order equals the Pinsker σ-algebra of the G-process; the proof is rigorous and uses relative entropy via the multiorder factor and a Z-action generated by the successor map. The model’s solution follows the paper’s structure but incorrectly assumes (without justification) that the multiorder factor has zero entropy under both the G- and the induced Z-actions, which is not true in general and is unnecessary for the theorem.