STRICT HÖLDER EQUIVALENCE OF SELF-SIMILAR SETS fileciteturn0file0

Yanfang Zhang, Xinhui Liu

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves exactly the three statements the model claims: (1) strict Hölder classification of totally disconnected fractal cubes by rationality of log N/log N′; (2) the snowflaking equivalence criterion linking strict Hölder to bi-Lipschitz via exponent s=dim_HE/dim_HF; and (3) the complete two-branch SSC classification, with the irrational case characterized by aligned ratios of logs and the rational case by the exceptional pair {2/3, 1/5}. The model’s approach mirrors the paper’s: symbolic coding, snowflaking, and invoking the Rao–Ruan–Wang two-branch Lipschitz classification. A minor gap appears in the model’s ‘necessity’ argument for symbolic spaces (a counting step is not rigorous), but it can be repaired by the same cited classification used in the paper. The paper contains minor presentation issues (a few typos and one misphrased ‘identity map’), but the mathematics is sound.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The results settle strict Hölder equivalence in two natural families by a clean reduction to symbolic models and known Lipschitz classification results. The techniques are standard but well-deployed; the contribution is to crystallize the snowflaking criterion and derive the precise two-branch classification. Minor typographical issues and a small wording slip should be corrected. With those fixes, the paper is a solid, publishable note in fractal geometry.