Irregular Fixation II: The orbits of irregular satellites

The paper proposes an empirically validated three-step energy-based classifier for Kozai–Lidov libration using Htot = Hsec + HB, including a specific Step (3) acceptance rule: if E−c < −0.1 or ΔE < 2, classify as librating. This rule is clearly stated and supported by the data presentation (Fig. 3 region occupancy) in the paper. By contrast, the model’s solution reverses the sign in Step (3), arguing that the ‘conservative’ condition should be E−c > −0.1. That change contradicts the paper’s explicit empirical finding that the region E−c < −0.1 or ΔE < 2 contains only librators. The model does correctly restate parts (a)–(b) and offers a reasonable heuristic bound linking min(E±c) > 0 to no separatrix crossing over an outer period, but its Step (3) reinterpretation is at odds with the paper’s stated and plotted criterion.