2508.16393
Counting the number of 2-periodic OK-points of a discrete dynamical system with applications from arithmetic statistics, V
Brian Kintu
incompletehigh confidence
- Category
- Not specified
- Journal tier
- Note/Short/Other
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper repeatedly conflates roots of φ^2(z)−z with genuine 2-periodic points (which also require φ(z)−z≠0), leading to uniform counts that are false; the candidate model spots non-uniformity but makes a fundamental exponent error (using 2p in place of p^2), so its formulas and some counterexamples are also incorrect.
Referee report (LaTeX)
\textbf{Recommendation:} reject
\textbf{Journal Tier:} note/short/other
\textbf{Justification:}
The paper’s central counting results (Theorems 2.2/2.3 and 3.2/3.3) are flawed: the proofs conflate roots of φ\^2(z)−z with 2-periodic points, ignoring the filter φ(z)−z≠0. Consequently, the asserted uniform counts are false. Substantive revision would require reworking the arguments using the additive-polynomial/trace framework and revising every subsequent density/average statement that depends on the incorrect counts. Given the extent of corrections needed, rejection is appropriate at this stage.