2407.04702
On the Nonexistence of Centered Co-Circular Central Configurations With Three Unequal masses
Zhengyang Tang, Shuqiang Zhu
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves the exact nonexistence claim via dihedral-symmetry and quadratic-form arguments, while the model correctly reduces the solver question to this theorem using the standard tangential/radial characterization and uniqueness of θ_m. The model, however, misattributes the paper’s proof technique to a layer-cake method.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The main result is of interest in the focused literature on co-circular central configurations and gives a clean nonexistence criterion extending previous patterns of equal masses. The argument is well structured using dihedral symmetry, a quadratic form, and a geometric inequality; the case analysis is systematic and appears correct. Minor editorial issues (e.g., repeated 'lose' for 'loss') and small clarifications would further improve readability, but no substantive mathematical gaps were found.