Dynamical covering sets in self-similar sets

The paper’s statements and proof architecture (probabilistic pressure L(s), upper bounds via expectation and Borel–Cantelli, and lower bounds including a martingale/large deviations regime for small α) are coherent and internally consistent with precise formulations of Theorems 1.2–1.3 and their phase transitions. In contrast, the candidate solution makes key incorrect or unjustified reductions: (i) it asserts a counting lemma CL2 claiming β_*:=liminf_m (1/m) log B_m ≥ α, which is false in general; (ii) it attempts to derive D_div ⊆ L_{β_*+δ} using an upper bound B_m ≤ e^{(β_*+o(1))m} that liminf does not supply; (iii) it does not construct a globally independent subsequence across levels to justify a second Borel–Cantelli argument; and (iv) it contains a sign error and a non-working lower-bound mechanism for the q<0 (negative moment) case used to characterise the complement. Consequently, while the model states conclusions matching the paper’s main theorems, its proof outline is flawed and incomplete, especially in the small-α regime where the paper’s martingale methods are essential.