CONTINUOUS ORBIT EQUIVALENCE RIGIDITY FOR LEFT-RIGHT WREATH PRODUCT ACTIONS

Jiang’s paper proves that for Γ1 finitely generated, non-torsion, non-amenable, and icc, the left-right wreath product action Z/pZ ≀_{Γ1}(Γ1×Γ1) on (Z/pZ)^{Γ1} is minimal, topologically free, and continuous orbit equivalence (COE) superrigid (Theorem 1.1) . Topological freeness is handled by Lemma 4.1 under a standing assumption that is satisfied by the left-right action; minimality follows because the base group fixes any finite pattern and hence has dense orbits; both are exactly as in the paper’s argument (Remark 4.2 + Lemma 4.1) . The heart of the paper’s COE superrigidity is Section 3 (continuous cocycle superrigidity for generalized full shifts, Theorem 3.3) together with the classification theorem for generalized wreath product actions (Theorem 4.4) and its prime-order corollary (Corollary 4.5) that yields conjugacy from COE in the p-prime case . By contrast, the model’s solution is correct on minimality and topological freeness, but its COE-superrigidity step is flawed. It claims, without support in the paper, that the wreath product action itself is continuous cocycle superrigid and that the target action in a COE is also cocycle superrigid “by symmetry”; the paper proves cocycle superrigidity for the generalized full shift Γ y X (not for the wreath product action) and then uses a dedicated classification argument to pass from COE to conjugacy (Theorem 4.4), avoiding the model’s bidirectional “untwisting” requirement . Hence the paper is correct and complete; the model’s central rigidity argument is incorrect/circular and does not follow from the cited results.