On the dynamical Mordell–Lang conjecture in positive characteristic

The paper’s main theorem (Theorem 1.5) proves that for any bounded-degree self-map f on a projective variety over an algebraically closed field of characteristic p>0, every return set R(x,V) is a widely p-normal set in N, not merely p-normal. This is stated explicitly and proved via (i) a regularization of bounded-degree maps to bounded-degree automorphisms (Theorem 4.6), (ii) the fact that bounded-degree automorphisms arise from algebraic group actions (Proposition 4.1), and (iii) the translation case where return sets are shown to be widely p-normal (Theorem 3.1) . Moreover, the paper explicitly disproves the earlier pDML formulation that predicted p-normal (not widely p-normal) return sets (Section 5) . By contrast, the candidate solution incorrectly cites the paper as proving p-normal and then adds a parity argument to reach widely p-normal; this misstates the result and relies on an unnecessary and only sketchily justified reduction. While the candidate’s final conclusion for bounded-degree maps (widely p-normal) matches the paper, the premise and citation are incorrect, and the extra reduction is not needed.