2210.09280
UNIFORM A PRIORI BOUNDS FOR NEUTRAL RENORMALIZATION.
Dzmitry Dudko, Mikhail Lyubich
correctmedium confidence
- Category
- Not specified
- Journal tier
- Top Field-Leading
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper explicitly defines W^+_3(I) and proves a uniform bound via a detailed pseudo‑Siegel disk/renormalization framework culminating in Theorems 10.1→1.1 (uniform in bounded type) . By contrast, the model’s write‑up asserts an unproved identity W^+_3(I)=mod(A(I)) for an ad hoc “butterfly collar” and then appeals to the very paper’s main theorem (“uniform pseudo‑Siegel a priori bounds”) as a black box to conclude the result. It bypasses the paper’s essential ingredients (external vs. diving decomposition, Covering/Amplification/Calibration lemmas, inductive construction of pseudo‑Siegel disks) that make the argument work . Hence the paper is correct, while the model’s solution is not a self‑contained proof.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} top field-leading
\textbf{Justification:}
A significant and technically strong result establishing uniform a priori bounds for bounded-type Siegel disks, removing the formerly standard high-type restriction. The construction of pseudo–Siegel disks and the combination of Covering/Amplification, Snake–Lair, and Calibration lemmas are thoughtfully orchestrated. The paper is long but well organized, with section-level outlines; a few additional navigational aids would improve readability for non-specialists.