2026/03/09 by Bernd von Mallinckrodt · 1 voice
paper · doi:10.5281/zenodo.18927395
openalex publication_date 2026/03/09 · openalex created_date 2026/03/10 · openalex updated_date 2026/07/01
This preprint introduces the Compression–Resonance–Tension Index (CRTI), a candidate diagnostic framework for assessing stability and fragility in complex adaptive systems (CAS). Across domains such as financial networks, ecological systems, technological infrastructures, and organizational structures, systemic collapse often follows a common structural trajectory: increasing efficiency and structural optimization reduce redundancy and adaptive capacity, while external stress accumulates. This process creates a latent fragility that can remain hidden until a critical threshold is crossed, triggering nonlinear breakdown. The CRTI framework proposes a dimensionless stability ratio defined as CRTI = (C + T) / R*** where: C* (Compression) represents structural concentration and loss of modular diversity T* (Tension) represents external or systemic stress imposed on the system R* (Resonance) represents adaptive capacity, redundancy, and latent system variety The framework hypothesizes that system stability depends on the balance between accumulated structural constraints and adaptive capacity. Collapse occurs when constraint accumulation exceeds adaptive reserve. A Lyapunov-style stability interpretation is proposed: V(t) = (C* + T*) − R* with stable systems satisfying V(t) < 0. Conceptually, the CRTI connects several theoretical traditions in complex systems science, including: Ashby’s Law of Requisite Variety Holling’s Resilience Theory Network percolation and fragmentation Critical transitions and early-warning signals Phase transition theory Retrospective pilot reconstructions suggest a common degradation sequence in complex systems: tinfo < tfunc < tstruct where informational distortion precedes functional degradation and structural breakdown. The proposed framework aims to provide a minimal diagnostic tool for identifying systemic fragility and early warning zones in complex adaptive systems. Future research should empirically test the CRTI across domains and operationalize the variables for quantitative measurement. If validated, the CRTI may contribute to a unified stability metric linking structural optimization, environmental stress, and adaptive reserve in complex systems. Keywords (für Zenodo extrem wichtig) Bitte diese Keywords eintragen: Keywords Complex Systems Complex Adaptive Systems Systemic Risk Systemic Fragility Resilience Theory Nonlinear Dynamics Early Warning Signals Network Collapse System Stability Adaptive Capacity Resilience Metrics Compression–Resonance–Tension Index CRTI Singularization Theory Mallinckrodt Cycle