POLYNOMIALS WITH CORE ENTROPY ZERO

Yusheng Luo, Insung Park

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves (1)–(4) in Theorem 1.1 and the complexity relations in Theorem 1.3 using the directed graph of the Hubbard tree, simplicial tuning/quotient, and relative hyperbolic components; the candidate solution follows the same combinatorial blueprint (Markov matrix/spectral radius, SCC depth, and tuning/quotient), and reaches the same conclusions. The only substantive discrepancy is that the candidate asserts a single simplicial tuning always increases Cgr by exactly 1, whereas the paper shows it can increase Cgr by 0 or 1, with exact unit decrease established for the inverse simplicial quotient (hence the equality Cgr=Cc is obtained via a quotient chain). Aside from this overstatement, the model’s arguments agree with the paper’s results and logic.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

This paper gives a crisp, multi-perspective characterization of core-entropy-zero PCF polynomials, unifying graph dynamics on Hubbard trees with parameter-space bifurcations and topological complexity. The proofs are sound and well-structured. One subtlety worth emphasizing more is the precise per-step effect of a single simplicial tuning on the growth complexity (0 or 1), contrasted with the exact unit drop for the simplicial quotient. The candidate solution mirrors the paper and is correct overall, with a small overstatement on that point.