2205.03734
Approximating linear response of physical chaos
Adam A. Śliwiak, Qiqi Wang
incompletemedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper argues, largely heuristically, that (i) aligning J with the most expansive unstable direction makes the leading unstable term small (via a leafwise integration-by-parts bound), (ii) the neutral leading term is then also negligible by comparability in a triad of near-zero exponents, and (iii) a reduced S3 algorithm keeping only the stable contribution performs well in high-dimensional, statistically homogeneous systems. These points are presented as conjectures with numerical evidence rather than full proofs . The model solution recasts (i)–(iii) into explicit L2 inequalities and a projected-tangent algorithm, but it introduces strong extra assumptions (e.g., an essential lower bound on g_m and tunable smallness of sup|g1| and ||∂_{q1} d||2) and a dimension-driven O(√{r/d}) bias claim not established in the paper. Hence both are incomplete: the paper lacks full rigor, and the model relies on unproven or unrealistic assumptions.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper advances a practical and numerically persuasive narrative: by aligning the observable and exploiting statistical homogeneity in high dimension, unstable and neutral pieces can be neglected and a reduced S3 algorithm suffices. However, the central claims remain conjectural: the smallness of the unstable and neutral leading terms lacks sharp, verifiable conditions and proofs; the dimension-driven penalty reduction is qualitative. Strengthening the mathematical backbone (even for stylized models) would materially raise the contribution.