2026/03/24 by von Mallinckrodt, Bernd · 1 voice
Environmental Science · #Ecosystem dynamics and resilience #Climate variability and models #Sustainability and Ecological Systems Analysis
paper · doi:10.5281/zenodo.19203579
openalex publication_date 2026/03/24 · openalex created_date 2026/03/25 · openalex updated_date 2026/07/01
This technical note documents a complete, falsification-first dry-run execution of the pre-registered CRTI (Compression–Response Thermodynamic Index) empirical validation pipeline (DOI: 10.5281/zenodo.19036931) on a structural analog dataset. The execution was conducted prior to real data access due to external network constraints in the runtime environment. All pipeline parameters were fixed ex ante and not modified post hoc, including window size (20), step size (1), first-difference detrending, z-score normalization, Φ(t) estimation via effective rank (spectral entropy of covariance), R(t) = 1 − AC1, and the composite index T(t) = R(t)/Φ(t). Statistical testing was performed using Kendall’s τ on the last 35% of the pre-transition window. The CRTI index T(t) did not exhibit a statistically significant trend in the pre-transition period (τ = −0.029, p = 0.638), while classical early warning indicators showed significant trends (Variance: τ = +0.166, p = 0.007; AC1: τ = −0.258, p < 0.001). The primary diagnostic finding is that Φ(t) remained nearly flat, limiting the sensitivity of T(t) despite detectable changes in R(t). This result is obtained on a structural analog dataset and does not constitute empirical validation on the Peter Lake dataset. The document provides an execution verification of the pre-registered pipeline, identifies a concrete estimator limitation (Φ sensitivity under weak covariance restructuring), and establishes a transparent baseline prior to real-data evaluation. The full pipeline, statistical protocol, and code are included without modification. CRTI, Compression-Response Thermodynamic Index, early warning signals, regime shifts, critical transitions, dynamical systems, ecological time series, pre-registration, falsification-first, effective rank, spectral entropy, Kendall tau, structural analog