On Fatou sets containing Baker omitted value

The paper’s Theorem 3.1 classifies the connectivity of Fatou components when a Baker omitted value lies in the Fatou set; its four parts match the model’s four assertions verbatim. The paper’s proof proceeds via: (i) properties of a bov (only asymptotic value; preimages of small disks are infinitely connected with bounded complementary components), (ii) Bolsch’s mapping dichotomy and properness on bounded Fatou components, and (iii) the Nayak–Zheng classification when all omitted values lie in one Fatou component. The model’s solution uses the same ingredients and structure. The only substantive flaw in the model write-up is the claim that f^{-1}(D) (for a small disk D around the bov) is itself a Fatou component; in the paper the key unbounded Fatou component is the preimage U^{-1} of the Fatou component U containing the bov, established via Lemma 2.4. This is a minor fix and does not affect the correctness of the conclusions.