Iterates of Meromorphic Functions on Escaping Fatou Components

The candidate solution proves exactly the conclusions of Theorem 2 in the uploaded paper under the same growth hypothesis (1.4) and the same annulus-in-orbit assumption. The paper’s proof builds a sequence of expanding round annuli via Lemma 6 (derived from [45]) and a hyperbolic annulus-covering lemma (Lemma 1), then establishes the existence and non-constancy of the harmonic limit h and the full-round-annulus images of small neighborhoods, as well as the comparative growth and nested-annulus conclusions (; ; ; ). The model’s argument follows the same strategy (annulus-to-annulus covering, annular bootstrap to infinity, convergence of normalized logs to a positive harmonic h, and local annular covering), with minor stylistic differences (e.g., invoking monomial-like or degree→∞ behavior instead of the paper’s explicit hyperbolic covering estimates). Substantively, they agree on all steps and conclusions (i)–(iv) of Theorem 2.