2207.11851
A SET OF 2-RECURRENCE WHOSE PERFECT SQUARES DO NOT FORM A SET OF MEASURABLE RECURRENCE
John T. Griesmer
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves Theorem 1.1, constructing a set S that is 2‑recurrent while S∧2 is not measurably recurrent, via Bohr–Hamming balls, compactness, and a gluing scheme; the candidate solution follows the same strategy and key lemmas (non‑recurrence of Bohr–Hamming balls and 2‑recurrence of their square roots, plus scaling and compactness) essentially line‑by‑line with only minor omissions in technical qualifiers (e.g., “proper” Bohr–Hamming balls and the total ergodicity reduction used to prove Lemma 3.5) .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The result settles a targeted open question for k=2 with a careful synthesis of finite gluing and deep ergodic-theoretic machinery. The argument appears correct and complete; suggested edits are mainly expository to guide readers through the technical reductions.