2026/04/19 by Bernd von Mallinckrodt · 1 voice
Environmental Science · Physics and Astronomy · Computer Science · #Ecosystem dynamics and resilience #Chaos control and synchronization #Seismology and Earthquake Studies
paper · doi:10.5281/zenodo.19649257
This paper serves as the entry point (Step 0) to the CRTI (Compression–Response Transition Index) framework, a structural–dynamic approach to early warning in complex systems. Classical early warning signals (EWS), such as variance and lag-1 autocorrelation, capture critical slowing down but remain blind to changes in the structural degrees of freedom of a system. CRTI complements this perspective by combining: Structural compression (Φ), derived from the spectral entropy of a rolling covariance matrix Recovery dynamics (R), estimated via short-horizon relaxation proxies into the composite indicator: T(t) = R(t) / Φ(t) This document does not introduce new theory. Instead, it provides: a clear statement of the underlying problem the minimal formal layer required to understand CRTI a positioning relative to classical EWS and related approaches a structured navigation map across the existing CRTI corpus The framework is explicitly scope-bounded and falsifiable. Documented limitations include the Relaxation-Coupling Failure Mode (RCFM) and the Structural Decoupling Sanity (SDS) condition, which must be satisfied for meaningful interpretation. The purpose of this paper is to make the CRTI framework navigable, understandable, and adoptable for researchers and practitioners working with complex systems approaching critical transitions. CRTI, early warning signals, critical transitions, complex systems, structural compression, spectral entropy, effective rank, covariance structure, multivariate analysis, critical slowing down, system stability, bifurcation, resilience, dynamical systems