SPIDERS’ WEBS IN THE EREMENKO–LYUBICH CLASS

The uploaded paper proves Theorem 1.2: A(cosh) is a spider’s web, by constructing a continuous surjection from Ĉ \ A(cosh) to Ĵ(g) \ A(g) using Pardo‑Simón’s topological model for cosine dynamics (Proposition 3.2), applying Evdoridou–Sixsmith’s theorem that Ĵ(g) \ A(g) is disconnected for the disjoint‑type map g(z)=cosh(z)/2 (Theorem 3.1), and invoking Sixsmith’s characterization that A(f) is a spider’s web iff it separates some point of J(f) from infinity (Theorem 3.3) . The candidate solution follows the same route: Sixsmith’s criterion, a Pardo‑Simón–type surjection preserving fast escape, and Evdoridou–Sixsmith’s disconnectedness of the complement, concluding that A(cosh) is a spider’s web. Minor phrasing differences (e.g., target codomain Ĵ(g) \ A(g) vs. Ĉ \ A(g); and ‘some finite point’ vs. ‘some point of J(f)’) do not affect correctness for cosh, since J(cosh)=C. Hence both are correct and essentially the same proof.