| _version_ | 1866901248542769152 |
|---|---|
| author | von Mallinckrodt, Bernd |
| author_facet | von Mallinckrodt, Bernd |
| contents | <p>This paper introduces the Compression–Response Transition Index (CRTI) as a dynamic–geometric coupling framework for early warning signals in complex systems.</p> <p>Classical early warning signals (EWS), particularly those based on critical slowing down (e.g., rising variance and lag-1 autocorrelation), are widely used but remain mechanism-agnostic and do not explicitly capture structural transformations of the system’s state space. The CRTI framework addresses this limitation by coupling two established signal classes: local recovery dynamics and global structural dimensionality.</p> <p>The dynamic component, R̂(t), is operationalized via lag-1 autocorrelation as a proxy for recovery rate, while the structural component, Φ(t), is derived from the spectral entropy of the covariance eigenvalue spectrum (effective rank formulation following Roy and Vetterli). Φ(t) is interpreted as the effective dimensionality of the system’s occupied state-space manifold.</p> <p>The resulting index, T(t) = R̂(t) / Φ(t), is dimensionless and can be interpreted via its logarithmic derivative as a relative growth rate of systemic risk:<br>d/dt ln T(t) = d/dt ln R̂(t) − d/dt ln Φ(t)</p> <p>The framework introduces a Structural–Dynamic Separability (SDS) condition to ensure non-redundant information content between R̂ and Φ, operationalized via low correlation or mutual information. A diagnosis cascade (Stage 1–3) describes the progression from hidden structural compression to functional singularization (topological rank collapse).</p> <p>The approach is explicitly constrained to non-equilibrium steady-state (NESS) regimes and mechanism-specific fold-type bifurcations, and assumes an adiabatic separation of timescales between structural evolution and recovery dynamics.</p> <p>CRTI is positioned as a diagnostic architecture rather than a new metric, providing a principled integration of dynamical systems theory and information geometry. The framework is data-intensive and relies on consistent windowing and preprocessing for robust estimation.</p> <p>This work establishes a formal, mechanism-aware perspective on early warning signals and provides a foundation for future empirical validation in ecological, financial, biological, and socio-technical systems.<br><br></p> <p>CRTI<br>Compression–Response Transition Index<br>dynamic–geometric coupling<br>structural compression<br>spectral entropy<br>effective rank<br>early warning signals<br>critical transitions<br>fold bifurcation<br>non-equilibrium systems<br>state-space manifold<br>functional singularization<br>topological rank collapse<br>structural–dynamic separability<br>complex systems<br>resilience indicators<br>multivariate early warning signals<br>system collapse detection<br>information geometry</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19437562 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | CRTI: A Dynamic–Geometric Coupling Framework for Mechanism-Specific Early Warning Signals in Complex Systems von Mallinckrodt, Bernd <p>This paper introduces the Compression–Response Transition Index (CRTI) as a dynamic–geometric coupling framework for early warning signals in complex systems.</p> <p>Classical early warning signals (EWS), particularly those based on critical slowing down (e.g., rising variance and lag-1 autocorrelation), are widely used but remain mechanism-agnostic and do not explicitly capture structural transformations of the system’s state space. The CRTI framework addresses this limitation by coupling two established signal classes: local recovery dynamics and global structural dimensionality.</p> <p>The dynamic component, R̂(t), is operationalized via lag-1 autocorrelation as a proxy for recovery rate, while the structural component, Φ(t), is derived from the spectral entropy of the covariance eigenvalue spectrum (effective rank formulation following Roy and Vetterli). Φ(t) is interpreted as the effective dimensionality of the system’s occupied state-space manifold.</p> <p>The resulting index, T(t) = R̂(t) / Φ(t), is dimensionless and can be interpreted via its logarithmic derivative as a relative growth rate of systemic risk:<br>d/dt ln T(t) = d/dt ln R̂(t) − d/dt ln Φ(t)</p> <p>The framework introduces a Structural–Dynamic Separability (SDS) condition to ensure non-redundant information content between R̂ and Φ, operationalized via low correlation or mutual information. A diagnosis cascade (Stage 1–3) describes the progression from hidden structural compression to functional singularization (topological rank collapse).</p> <p>The approach is explicitly constrained to non-equilibrium steady-state (NESS) regimes and mechanism-specific fold-type bifurcations, and assumes an adiabatic separation of timescales between structural evolution and recovery dynamics.</p> <p>CRTI is positioned as a diagnostic architecture rather than a new metric, providing a principled integration of dynamical systems theory and information geometry. The framework is data-intensive and relies on consistent windowing and preprocessing for robust estimation.</p> <p>This work establishes a formal, mechanism-aware perspective on early warning signals and provides a foundation for future empirical validation in ecological, financial, biological, and socio-technical systems.<br><br></p> <p>CRTI<br>Compression–Response Transition Index<br>dynamic–geometric coupling<br>structural compression<br>spectral entropy<br>effective rank<br>early warning signals<br>critical transitions<br>fold bifurcation<br>non-equilibrium systems<br>state-space manifold<br>functional singularization<br>topological rank collapse<br>structural–dynamic separability<br>complex systems<br>resilience indicators<br>multivariate early warning signals<br>system collapse detection<br>information geometry</p> |
| title | CRTI: A Dynamic–Geometric Coupling Framework for Mechanism-Specific Early Warning Signals in Complex Systems |
| url | https://doi.org/10.5281/zenodo.19437562 |