The Compression–Resonance–Tension Index (CRTI): A Stability Diagnostic for Complex Adaptive Systems

This research note introduces the Compression–Resonance–Tension Index (CRTI) as a diagnostic stability parameter within the Meta-Model of Singularization (V3.0). The framework proposes that systemic collapse in complex adaptive systems (CAS) is frequently driven not by disorder or entropy, but by structural over-order—a progressive compression of internal variance that suppresses adaptive resonance with the environment. In highly optimized systems, the elimination of redundancy and diversity can lead to a robust-yet-fragile (RYF) configuration in which efficiency increases while resilience decreases. The CRTI formalizes this dynamic by conceptualizing systemic stability as a balance between three interacting components: compression (C), representing structural rigidification and loss of internal degrees of freedom; resonance (R), describing the system’s capacity for adaptive coupling and information exchange with its environment; and tension (T), representing accumulated systemic stress arising from mismatches between internal structures and external conditions. In its conceptual form, the CRTI can be expressed as: CRTI = (C * T) / R Low CRTI values indicate systems with sufficient structural variance and feedback permeability to absorb disturbances, while high CRTI values characterize systems approaching singularization, a state of brittle rigidity in which small perturbations can trigger disproportionate collapse. The framework integrates insights from information theory, network science, nonlinear dynamics, and cybernetics, and connects to established concepts such as Ashby’s Law of Requisite Variety, Kauffman’s edge of chaos, Prigogine’s dissipative structures, and the robust-yet-fragile paradigm. Potential applications include the diagnosis of systemic fragility in organizations, ecosystems, financial systems, and socio-technical networks. The CRTI is proposed as a conceptual stability diagnostic and a starting point for further mathematical formalization and empirical testing across domains of complexity science. Keywords (optimal für Scholar) Complex Adaptive Systems CRTI Singularization Systemic Stability Complex Systems Theory Cybernetics Information Theory Nonlinear Dynamics Network Theory Resilience Robust-Yet-Fragile Systems Systemic Risk Socio-Technical Systems Early Warning Signals Systems Engineering Adaptive Systems Structural Fragility Complexity Science Organizational Systems Ecological Resilience