Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy

The paper proves: (i) mean stability is equivalent to all minimal sets being attracting (Lemmas 3.8–3.9), (ii) attracting minimal sets persist under small perturbations (Lemma 3.13), yielding openness of A(X) (Proposition 3.14 ⇒ Corollary 3.16), and (iii) under condition (*), A(X) ∪ C(X) is dense (Theorem 3.21, with C(X) defined by Ji(Sτ)=Ĉ for all i and the strong hitting property). The candidate solution outlines exactly this chain—using the same characterizations and perturbation arguments—so it matches the paper’s method. Minor issues are small numbering slips (e.g., calling the equivalence a corollary and citing Corollary 3.15 vs 3.16; Theorem 3.22 vs 3.21), but the logical content aligns with the paper’s proofs and assumptions, including the MRDS topology and irreducibility. Key steps and conclusions are consistent with the uploaded paper .