The Exact Value of Hausdorff Dimension of Escaping Sets of Class B Meromorphic Functions

The paper proves HD(I(f)) = lim_{R→∞} HD(IR(f)) = δ for f ∈ B with no asymptotic value at ∞ and uniformly bounded pole orders (Theorem 1.3), via an upper bound from natural covers and a lower bound using a carefully constructed non‑autonomous IFS after a desingularizing change of variables u(ξ)=ξ^{-M} and triple compositions Φ_{l,j} ensuring bounded distortion and uniform contraction; see the statement of Theorem 1.3 and its proof outline, Proposition 3.4, Lemma 5.3–5.4, and Theorem 4.1 summarized in the paper . By contrast, the candidate asserts (i) HD(IR(f)) = δ for all sufficiently large R and (ii) HD(ER(f)) = HD(X_R) by a purported uniform bi‑Lipschitz transfer; both are unsupported. In fact, the paper notes that often HD(IR(f)) > δ for every R > 0, even though lim_{R→∞} HD(IR(f)) = δ (Remark 7.5), contradicting the model’s claim of equality for large R .