JULIA SETS AND GEOMETRICALLY FINITE MAPS OVER FINITE EXTENSIONS OF THE p-ADIC FIELD

The paper proves JCp(φ) ∩ P1_K = JK(φ) under assumptions (1) no wild recurrent critical points in JCp(φ) ∩ P1_K and (2) each minimal class has ≤2 representatives there, via a careful reduction to Julia-critical points and a construction of repelling (pre)periodic points in specific K-disks (Propositions 3.7, 3.8, 3.10; Corollaries 3.9, 3.11), together with boundary and diameter-control lemmas (Lemmas 3.1, 3.2) and a reduction (Proposition 3.4) . The candidate solution reaches the same conclusion but assumes a stronger claim (“every K-disk in JCp(φ) ∩ P1_K contains a K-repelling periodic point”), and cites it as a theorem. That statement is not presented verbatim in the paper; instead, the paper proves existence of (pre)repelling points in carefully chosen disks near critical orbits to force non-equicontinuity. Thus, while the conclusion matches and the high-level mechanism (repelling points force JK-membership) aligns with the paper’s strategy , the candidate’s argument overstates what is proven locally and misnumbers the cited result. Overall, both are correct on the main equality, but the paper’s proof is more precise and complete.