2209.13810
Non-Integrability of the Trapped Ionic System II
Georgi Georgiev
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper states a broad non‑integrability theorem and correctly derives the NVE on the invariant plane and the exponent gap p = sqrt(1+4F/E), proving (a) via branching, but its proof of (b) misuses the Baider–Churchill invariants (it concludes t∞ is transcendental over Q even though cos(π·rational) is algebraic), and most of (c) is asserted without full derivations beyond c.0) . The model’s outline uses the standard Morales–Ramis–Simó program and gets the same structure and parameter p; its treatments of (a)–(b) are plausible, but it does not actually exhibit the residue computations required for the many c.* subcases, so it also falls short of a complete proof.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript tackles a natural family and uses a recognized methodology. Part (a) is sound and the overall program is promising. However, the proof of (b) is incorrect as written (it misinterprets algebraicity vs transcendence for 2cos(πp)), and the extensive list of c.* subcases is stated without full derivations except for one illustrative example. Substantial additions are needed to render the claims verifiable and correct.