The Compression–Resonance–Tension Index (CRTI): A Minimal Dynamical Framework for Efficiency-Driven Collapse in Complex Adaptive Systems

This publication introduces the Compression–Resonance–Tension Index (CRTI), a minimal nonlinear dynamical framework for analyzing systemic collapse in complex adaptive systems. Traditional models in complexity science often interpret systemic failure as a consequence of increasing disorder, stochastic shocks, or entropy accumulation. The CRTI framework proposes an alternative endogenous mechanism: efficiency-driven collapse, where structural optimization progressively consumes the adaptive reserves required for resilience. The model formalizes the interaction between two fundamental variables: • Structural Compression (Φ) – representing systemic optimization pressure, efficiency, and structural load. • Adaptive Reserve (Ω) – representing redundancy, variance capacity, and regenerative buffers that enable systems to absorb perturbations. Within this framework, systemic stability emerges from the dynamic balance between structural organization and adaptive reserve capacity. As long as reserves regenerate sufficiently, the system remains within a stable region referred to as the Resonant Corridor. However, when structural pressure persistently exceeds the regenerative capacity of the adaptive reserve, the system approaches a critical transition. This process—termed Singularization—occurs when adaptive reserve is depleted to a point where the system loses its ability to respond to perturbations. The dynamical interaction between Φ and Ω is modeled through a minimal system of coupled nonlinear differential equations. Mathematical analysis shows that collapse occurs through a saddle-node bifurcation, where the stable equilibrium and an unstable saddle point collide and annihilate, eliminating the system’s stability basin. To detect this structural fragility, the framework introduces a dimensionless diagnostic indicator: χ = Φ / Ω Increasing values of χ indicate rising systemic tension and decreasing resilience. Unlike classical statistical early warning signals—such as rising autocorrelation or variance—the CRTI indicator directly measures the structural cause of systemic fragility: the depletion of adaptive reserve under increasing optimization pressure. To explore empirical applicability, a validation workflow is proposed using publicly available Federal Reserve Economic Data (FRED) surrounding the 2008 financial crisis. In this case study: • financial leverage proxies represent structural compression (Φ) • liquidity buffers represent adaptive reserve (Ω) Preliminary analysis suggests that the CRTI indicator identifies the structural decoupling between systemic load and reserve capacity well before the visible collapse of the financial system. Because the Φ–Ω interaction describes a fundamental trade-off between efficiency and resilience, the CRTI framework can be applied across multiple domains of complex systems, including: • financial systems (leverage vs liquidity buffers) • ecological systems (monoculture vs biodiversity) • supply chains (throughput vs redundancy) • infrastructure networks (utilization vs backup capacity) • neural systems (synchronization vs signal entropy) The CRTI model therefore functions as a minimal cross-domain dynamical template for efficiency-driven collapse in complex adaptive systems. Keywords (Zenodo) CRTI Complex Adaptive Systems Systemic Collapse Resilience Theory Nonlinear Dynamics Bifurcation Theory Structural Compression Adaptive Reserve Efficiency-Resilience Trade-off Critical Transitions Early Warning Signals Singularization