Measuring chaos in the Lorenz and Rössler models: Fidelity tests for reservoir computing.

The paper defines simple binary partitions for Lorenz (flip–flop at x′=0 by wing) and Rössler (z-max threshold) and empirically shows that source entropy h_m, LZ, and Markov transitions detect stability windows (vanishing on periodic orbits) and broadly track a normalized Lyapunov rate across parameter sweeps; it also validates RC surrogates using z_max return maps with the canonical cusp at r≈28 and the loss of expansion at higher r. These claims are documented and consistent within the paper’s computational scope, but not proved as theorems and rely on non-generating partitions and finite-N corrections . The model’s solution agrees on core points (periodic windows ⇒ h=0 and LZ→0; rational, constant Markov matrices; qualitative return-map checks) and adds reasonable theoretical context (LZ consistency, Ruelle inequality). However, it overstates some results with quantified guarantees (e.g., asserting strictly positive cross-parameter correlations and sup-norm return-map closeness implying persistence/exclusion of periodic points) that require stronger hypotheses than given in the paper and are not established there. Hence, both are incomplete: the paper is empirically correct but not formally proved; the model is largely correct conceptually but includes claims that exceed what is supported.