2026/03/24 by von Mallinckrodt, Bernd · 1 voice
Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #Chaos control and synchronization #Complex Systems and Dynamics
paper · doi:10.5281/zenodo.19204303
openalex publication_date 2026/03/24 · openalex created_date 2026/03/25 · openalex updated_date 2026/07/01
This technical note reports a pre-registered, falsification-first dry run of the CRTI (Compression–Response Thermodynamic Index) empirical validation pipeline on a structural analog dataset with a known regime transition. The composite index T(t) = R(t)/Φ(t), combining structural compression (estimated via effective rank of the rolling covariance matrix) and adaptive response capacity (defined as R(t) = 1 - AC1), shows no statistically significant pre-transition trend under the pre-specified pipeline configuration (Kendall’s τ = -0.029, p = 0.638). In contrast, classical early warning signals behave as expected: variance increases significantly and lag-1 autocorrelation exhibits a significant trend consistent with critical slowing down. This null result is not interpreted as stochastic failure, but as a mechanism-dependent limitation of the composite index. In Ornstein–Uhlenbeck-type dynamics, covariance structure and autocorrelation decay are co-determined by the same dominant relaxation process, rendering Φ(t) and R(t) partially redundant rather than informationally orthogonal. Under this condition, the ratio T(t) = R/Φ loses discriminative power. We formalize this condition as the Relaxation-Coupling Failure Mode (RCFM) and identify structural–dynamic separability as a necessary precondition for composite early warning signals to provide additional information beyond classical indicators. This result establishes a boundary condition of CRTI applicability prior to real-data deployment (Peter Lake eutrophication system), consistent with the pre-registered falsification protocol. More broadly, it suggests that composite early warning indicators should include a pre-deployment analysis of the coupling geometry between their components. CRTI early warning signals composite indicators critical slowing down Ornstein–Uhlenbeck process structural compression adaptive response capacity effective rank covariance structure Lyapunov equation multivariate early warning signals Fisher Information regime shifts complex systems falsification-first pre-registration Relaxation-Coupling Failure Mode structural–dynamic separability