CRTI: A Mechanism-Specific Measurement Framework for Early Warning Signals Based on Structural Compression in Fold Bifurcations The Compression–Response Transition Index (CRTI) is a mechanism-specific measurement framework for detecting early warning signals (EWS) in complex systems approaching fold (saddle-node) bifurcations.   Classical EWS—such as variance and lag-1 autocorrelation—capture changes in dynamic memory but do not resolve the geometric reorganisation of multivariate system states. CRTI addresses this limitation by introducing structural compression Φ(t), derived from the spectral entropy of the covariance matrix, as a scale-invariant measure of effective dimensionality. This structural component is combined with an adaptive response measure R(t), based on an AR(1) recovery proxy, into a composite index T(t) = R(t) / Φ(t).   Under explicitly stated domain-of-validity conditions—fold bifurcation dynamics, additive approximately isotropic noise, and multivariate observability (d ≥ 2)—CRTI yields a falsifiable prediction: the composite index T(t) decreases toward zero as the system approaches a critical transition.   A central methodological contribution is the introduction of the Structural–Dynamic Separability (SDS) condition, defined via the correlation between R(t) and Φ(t). If separability is violated (|ρ| ≥ θ), the composite index is declared invalid. The Relaxation–Coupling Failure Mode (RCFM) is identified as the primary mechanism underlying SDS failure.   CRTI is not proposed as a universal indicator but as a domain-restricted, validity-gated measurement instrument. Its applicability, assumptions, and limitations—including projection-induced distortion (PID), noise anisotropy, dimensionality constraints, and windowing artefacts—are explicitly defined.   This work provides a structured extension to the early warning signal framework by incorporating covariance geometry alongside classical dynamical indicators, enabling more specific detection of structural precursors in systems approaching fold-type critical transitions.   early warning signals critical transitions fold bifurcation structural compression spectral entropy covariance geometry AR(1) complex systems tipping points dynamical systems multivariate analysis system stability

What if systems don’t become unstable when variance rises…

but when they quietly lose their degrees of freedom?

Most early warning signals miss this …

they track noise, not structure.

CRTI measures that missing dimension.

→ doi.org/10.5281/zeno...

#CRTI #EarlyWarningSignals 🖖

CRTI: A Mechanism-Specific Measurement Framework for Early Warning Signals Based on Structural Compression in Fold Bifurcations The Compression–Response Transition Index (CRTI) is a mechanism-specific measurement framework for detecting early warning signals (EWS) in complex systems approaching fold (saddle-node) bifurcations....

What if systems don’t become unstable when variance rises …

but when they quietly lose their degrees of freedom?

#CRTI …

structural compression Φ(t) as missing dimension of #EarlyWarningSignals #EWS & defines falsifiable, validity-gated measure for fold bifurcations

→ doi.org/10.5281/zeno... 🖖

Compression–Response Transition Index (CRTI): A Mechanism-Specific Early Warning Signal for Fold-Type Critical Transitions This preprint introduces the Compression–Response Transition Index (CRTI), a bivariate early warning signal designed for detecting fold-type critical transitions in multivariate dynamical systems. The...

CRTI = R̂ / Φ couples recovery dynamics with covariance geometry …

and detects fold-type transitions earlier while correctly failing outside its domain.
Preprint (open access): doi.org/10.5281/zeno... 🖖

#CRTI #ComplexSystems #EarlyWarningSignals #NonlinearDynamics #EWS #SystemsScience 🖖

Mechanism-Dependent Sensitivity in Early Warning Signals: Boundary Conditions of Ratio-Based Composite Indicators This preprint investigates the behavior of ratio-based composite early warning indicators of the form T(t) = R(t)/Φ(t) in complex dynamical systems. Here, R(t) represents adaptive response capacity, w...

Classical #EarlyWarningSignals messen Amplitude …

aber was passiert mit der Struktur eines Systems vor dem Kollaps?

Ratio-basierte Indikatoren sind nicht „besser“, sondern messen eine andere Klasse von Information …

mit klaren Grenzen und Konsequenzen für ihre Anwendung.
doi.org/10.5281/zeno... 🖖

Singularization Framework v4: Bifurcation Structure, Stochastic Collapse, and Early Warning Signals in the CRTI Minimal Model This paper presents Version 4 of the Singularization Framework, a minimal dynamical theory of structural collapse in complex adaptive systems. The framework introduces three state variables — Structur...

Collapse rarely begins with chaos …

it begins when systems become too stable to adapt.

#CRTIv4 shows how bifurcation structure, stochastic escape, & early-warning signals reveal the collapse basin before the tipping point.
doi.org/10.5281/zeno...

#CRTI #ComplexSystems #EarlyWarningSignals 🖖

Excited to share our work in collaboration with @pik-potsdam.bsky.social and National Physical Laboratory, published in Scientific Reports. We show that early warnings are too late when parameters change rapidly.
10.1038/s41598-025-06525-5
#Tipping #EarlyWarningSignals #ComplexSystems #IITmadras

Way past #earlywarningsignals

#mathematicalModelling #drylandClimate #FairyCircles #phenology #badlands #AI #ML #NDVI #feedbackMechanisms #runoff #MCMCalgorithms #diffusion #bifurcations #tippingpoints #earlyWarningSignals

Key point: Antiseizure medication efficacy assessment based on change in seizure frequency is influenced by intrinsic seizure variability, especially at low SFs;
doi.org/10.1111/epi....

#epilepsy #epilepsia #ilae #complexsystems #earlywarningsignals #nonlinearanalysis #RQA #seizuresusceptibility