REALIZING POLYNOMIAL PORTRAITS

The paper proves the existence theorem: every abstract polynomial portrait Γ is realized by a polynomial f with Γ_f ≃ Γ (stated as Theorem 1 and outlined explicitly: construct an unobstructed topological polynomial via a finite subdivision rule and then apply Thurston’s characterization; the fixed vertex of full degree ensures the rational map is a polynomial) . The model solution cites precisely this FKKPS result and sketches the standard three-step route (topological model → no Levy obstruction → Thurston straightening to a polynomial). One small mismatch: the model attributes the construction to a “rose map,” whereas the paper’s proof of Theorem 1 uses a finite-subdivision-rule construction to forbid Levy cycles (via Lemma 6 and the ‘stickers’/new edges argument) rather than the rose-map setup used later for constructing obstructed examples . Substantively, however, both rely on the same unobstructedness + Thurston pipeline, so the conclusions agree.