2102.07283
STABLE INTERSECTIONS OF REGULAR CONFORMAL CANTOR SETS WITH LARGE HAUSDORFF DIMENSIONS
Alex Zamudio, Carlos Gustavo Moreira, Hugo Araújo
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper rigorously proves openness and density of U and the density of Is in I (hence int(K−K′)≠∅) via recurrent compact sets plus a periodic-scale density lemma; the candidate solution incorrectly claims an equivalence between “U holds” and “there exists a recurrent compact set,” and leans on this unproven equivalence for openness and density. While many components match the paper, that key step is unjustified and likely false in general.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
Solid, well-structured extension of stable intersection theory to the complex conformal setting with rigorous proofs of openness and density and a clear path from recurrent compacts to stable intersections. A few clarifications (notational roadmaps, highlighting the periodic-scale density step) would improve accessibility but do not affect correctness.