Generic behavior of differentially positive systems on a globally orderable Riemannian manifold

Lin Niu, Yi Wang

incompletemedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s introduction states Theorem A under (H1)–(H3), but the detailed proof (Theorem 3.1) additionally assumes a C∞-section of the cone field and a compactness condition (P), and the preliminaries globally assume precompact orbits; these are not entailed by (H1)–(H3) alone . The model asserts generic convergence from SDP/SOP without these extra compactness and regularity hypotheses and treats Γ-invariance as sufficient, which the paper’s proof strategy contradicts. Hence both are incomplete: the paper overstates Theorem A in the introduction, and the model omits crucial assumptions.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript addresses a timely question in differential positivity and provides a rigorous generic-convergence result for SDP flows on globally orderable manifolds, leveraging PF fields and Γ-invariance. The technical core appears sound, but the presentation overstates the main theorem in the introduction (Theorem A) relative to the hypotheses actually used in Theorem 3.1. Clarifying the precise assumptions (compactness (P), smooth cone-section, and the global precompactness adopted in the preliminaries) would align the statement with the proof and improve readability.