2026/04/06 by Bernd von Mallinckrodt · 1 voice
Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Climate variability and models #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19437325
openalex publication_date 2026/04/06 · openalex created_date 2026/04/07 · openalex updated_date 2026/07/01
This preprint introduces the Compression–Response Transition Index (CRTI) framework, a structural–dynamic diagnostic architecture for early warning signals in complex systems. Classical early warning signals (EWS), particularly those based on critical slowing down (CSD) such as rising autocorrelation (AR(1)) and variance, are widely used but remain mechanism-agnostic. They provide limited insight into the structural conditions underlying loss of resilience and cannot reliably distinguish between different bifurcation types. The CRTI framework addresses this limitation by coupling two established but previously uncoupled signal classes:(1) Structural Compression (Φ), operationalized via spectral entropy of the covariance matrix using the effective-rank formulation of Roy and Vetterli, and(2) Response Capacity (R̂), estimated as a recovery-rate proxy derived from lag-1 autocorrelation. The diagnostic index T = R̂ / Φ emerges from this structural–dynamic coupling and is valid only under a formally defined Structural–Dynamic Separability (SDS) condition, which ensures that both components carry independent information. The framework further introduces a diagnosis cascade describing the progression of system states from full-dimensional dynamics through structural compression to functional singularization, defined as the loss of effective degrees of freedom in system response space. Importantly, this work does not propose new fundamental metrics. Its contribution lies in the integration of existing methods into a mechanism-specific diagnostic framework, explicitly restricted to fold-type (saddle-node) bifurcation regimes and bounded by testable validity conditions. The CRTI framework is positioned as a complementary approach to existing early warning methodologies and provides a structured basis for future empirical validation across ecological, climatic, financial, and biological systems. CRTICompression–Response Transition Indexstructural compressionspectral entropyeffective rankearly warning signalscritical transitionsfold bifurcationcovariance dynamicsfunctional singularizationstructural–dynamic separabilitycomplex systemsresilience indicatorsmultivariate early warning signalssystem collapse detection