A CONVERSE OF DYNAMICAL MORDELL–LANG CONJECTURE IN POSITIVE CHARACTERISTIC

The paper’s main theorem explicitly proves that any subset of N0 that is a finite union of arithmetic progressions and p-sets is an Fp(t)-DML set over a split torus (Theorem 1.6) and reduces the proof to a special case (Theorem 3.1) using Lemmas 2.1–2.3; arithmetic progressions are handled by Lemma 2.2, and closure under unions, scalings, and translations by Lemmas 2.1 and 2.3. The special case is then proved by decomposing into p-sets to which the Corvaja–Ghioca–Scanlon–Zannier bound applies, combined via an induction with Lemma 3.4; field change to Fp(t) is handled by Lemma 3.2. These steps are present and coherent in the PDF (Theorem 1.6, Lemmas 2.1–2.3, Theorem 3.1, Lemma 3.4, and the use of [CGSZ] in Theorem 1.5) . By contrast, the model’s solution misstates the small-coefficient condition needed for the CGSZ realization (it claims a threshold ∑cj ≤ q−1 via a “no-carry” normalization, whereas the paper correctly uses the stricter ∑cj < q/2 bound), and attributes a base-q digit carry argument to Lee–Nam that is not how the paper proceeds; it also overstates that all maps used are monomial endomorphisms. Hence, while the high-level structure aligns, the model’s core normalization step and citation of the threshold are incorrect.