IMMEDIATE RENORMALIZATION OF COMPLEX POLYNOMIALS

The paper proves the stated recurrence theorem under the explicit hypothesis of empty rational lamination (Theorem 1.2) with a detailed argument that leverages decorations, sectors, backward stability, and a local connectivity result to derive a contradiction if the outer critical point were non-recurrent . By contrast, the model reduces the claim to a different hypothesis (“no (pre)periodic cutpoints”) and then asserts that empty rational lamination forbids (pre)periodic cutpoints, citing only the general landing theorem. That implication requires deeper topological input (e.g., results on cutpoints and multiple ray landings) that the model does not supply; Milnor’s landing theorem alone is insufficient. Hence the model’s argument is incomplete/invalid as stated, while the paper’s proof is correct.