2026/04/03 · 1 voice
Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #Chaos control and synchronization #stochastic dynamics and bifurcation
paper · doi:10.5281/zenodo.19410081
This paper serves as the primary reference for the structural compression (Φ) framework. All related extensions, applications, and methodological refinements build upon this core formulation. Description Classical early warning signals (EWS) for critical transitions rely primarily on amplitude-based indicators such as variance increase and autocorrelation (critical slowing down). These approaches implicitly assume that structural deterioration in a system manifests as observable changes in marginal variance. This work identifies and formalizes a complementary failure mode: systems can approach collapse through a loss of effective degrees of freedom while total variance remains approximately constant. In such cases, classical indicators remain silent by construction. We introduce a mechanism-specific diagnostic framework based on structural compression (Φ), defined as the exponential spectral entropy of the covariance eigenvalue distribution, and dynamic responsiveness (R), a measure of recovery capacity. The viability ratio T = R/Φ captures the balance between adaptive capacity and structural rigidity. Under the Structural–Dynamic Decoupling (SDD) condition (increasing Φ, decreasing R), a monotone decline in T constitutes a pre-bifurcation signature that can precede variance-based signals. The framework further incorporates a detectability constraint through Projection-Induced Determinism (PID), formalized via the alignment-dependent bound V* = Φ · A, which specifies when structural signals are observable in low-dimensional projections. This approach is explicitly mechanism-specific and restricted to fold-type bifurcations under additive noise in multivariate systems. It does not apply to Hopf bifurcations, noise-induced transitions, or rate-induced tipping. Its primary contribution is to provide a falsifiable, geometry-based extension to classical early warning signals, targeting collapse dynamics that remain undetected by amplitude-based methods. --- Keywords early warning signals; critical transitions; critical slowing down; structural compression; spectral entropy; covariance eigenvalues; multivariate systems; bifurcation theory; fold bifurcation; system collapse; dimensionality reduction; effective rank; complexity science; nonlinear dynamics; resilience; tipping points; projection effects; observability; information geometry; complex systems