The simplest chaos indicator derived from Lagrangian descriptors

The paper gives only a heuristic derivation of the ∆L bounds for the arclength LD—expanding fi(x′) to first order, linearizing the square root, and substituting |δx_i(t)| ≈ |β| e^{λ_i(t−t0)}—without controlling remainders or addressing degeneracies (e.g., division by ∥f∥ near slow points), and it contains an algebraic slip in the p-norm appendix where a factor p is missing in the denominator of the final bound (its Eq. (35)) . The model’s main arclength proof is substantially sound—deriving a finite-window bound from a Lipschitz estimate for F(x)=∥f(x)∥ and the variational flow—yet its optional Hölder-style estimate for the p-norm uses an incorrect inequality for 0<p≤1. Hence, both treatments are incomplete: the paper’s argument is heuristic and overlooks edge cases, and the model’s optional p-norm addendum has a technical flaw.