Mn is connected

The paper explicitly proves Main result A: for each n, the connectedness locus Mn for fractal n-gons is connected, via a general theorem (Theorem 3.3) about zero sets of power series with coefficients in a finite set G satisfying condition (*), together with the identification Mn = X_{Ω_n} and the annulus inclusion {1/√n < |z| < 1} ⊂ Mn from Bandt–Hung (Lemmas 4.5 and 4.6), and verification that Ω_n satisfies condition (*) (Theorems 4.7 and 4.8) . By contrast, the candidate solution replaces the paper’s condition (*) with an unreferenced “coefficient-graph” Γ(G) connectivity hypothesis, misidentifies the coefficient set as G = V − V instead of the normalized Ω_n = {(ξ^j − ξ^k)/(1 − ξ_n)}, and wrongly attributes a stronger “indeed locally connected” conclusion to Nakajima’s theorem. None of these substitutions appear in the paper’s framework, which requires 1 ∈ G and the closure property (b_{i+1} − b_i)c + d ∈ G (for all c ∈ G, some d ∈ G), not mere graph connectivity . Hence the paper’s argument is sound as written, while the model’s proof is not a correct rendering of the paper’s method or hypotheses.