Adding machines and open dynamical systems

The paper proves residual indecisiveness on the minimal Cantor part Q of a genus‑1 maximal ω‑limit set, then asserts it is residual on ω(x)=Q ⊔ C “as C is countable,” but C consists of isolated (hence open) points, so countability alone does not make C meager; the extension step is unjustified (structure of ω(x) and the Q ⊔ C decomposition is recalled in the paper’s Section 1, and Theorem 12’s proof contains this step). Definition 3 also appears to have a typo, taking an intersection over j=1,2,… instead of i=1,…,N. The model’s solution, while giving a plausible odometer/partition-based argument, incorrectly assumes ω(x) itself is a Cantor minimal set (it can have a countable set of isolated points), and it never addresses those isolated points. Therefore, both arguments have gaps. See the paper’s definitions/results and the solenoidal-set structure: Definition 3 and 6; Theorem 12 and its proof; and the description of ω(x)=Q ⊔ C with C countable and consisting of isolated points.