2412.13759
Iterated Relation Systems on Riemannian Manifolds
Jie Liu, Sze-Man Ngai, Lei Ouyang
correcthigh confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s main dimension formula under GOSC/GFTC is stated correctly and tied to prior results (proofs largely omitted but standard), while the candidate solution supplies a direct Perron–Frobenius/Frostman argument. Aside from a minor notational glitch in (4.1) and a misleading curvature remark, the statements align. The model’s proof matches the classical Mauldin–Williams scheme adapted to a Riemannian setting and is coherent with the paper’s framework.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The article develops a flexible IRS-to-GIFS framework on manifolds and states clean dimension results under GOSC/GFTC, backed by prior literature. The theory is correctly positioned and supported by examples. Minor issues—an imprecise incidence-matrix display and a curvature remark—should be corrected, and brief proof sketches would enhance self-containment. These do not affect correctness but will improve clarity and usability.