A Case Study on Identifying Bifurcation and Chaos with CROCKER Plots

The paper specifies a concrete pipeline (Ripser-based Vietoris–Rips persistence, per-parameter d_max, N=100 ε samples, CROCKER matrices) and reports strong Pearson correlations between the L1 norm of Betti vectors and the maximum Lyapunov exponent for both Rössler and Lorenz, along with qualitative CROCKER features (e.g., a structural change near a≈0.41 and ρ≈92.5 vs ≈100), all documented in the Methods and Results sections . The candidate solution did not implement true VR persistent homology in H1 (using a 1-skeleton cyclomatic proxy) and, even for H0 where MST-based persistence is exact, produced correlations far from the paper’s values; the explanation offered (ε-normalization) does not reconcile with the paper’s per-parameter d_max protocol. Hence, the paper’s claims are supported by its stated method, while the model’s computations are methodologically inconsistent with the paper and numerically off.