Topological groups with tractable minimal dynamics

The paper’s Theorem 9.20 rigorously proves the equivalences between TMD/CMD/EA and the existence of G-skeletons with minimality+ED+Ramsey (and precompactness in the CMD case), and identifies X_Ω ≅ M(G) under these hypotheses. The model’s write-up tries to rederive these results but makes essential missteps: it incorrectly builds a skeleton whose levels are all M(G) with identity bonding maps (violating the skeleton definition that requires level metrics to be compatible and, in practice, to be the ∂σ-quotient with compatibility points), gives a flawed “single g works for all coordinates” argument for minimality, implicitly uses an infinite join in the semilattice when only finite joins are available, and replaces the paper’s central Ramsey⇒M(G) equivalence (Theorem 9.19) with an undeveloped universality argument. The conclusions match the paper, but the proof is not sound.