The Singularization of Complex Adaptive Systems: A Structural Diagnostic Framework for Systemic Fragility

This preprint introduces the Singularization Framework, a diagnostic model for identifying structural fragility in complex adaptive systems (CAS). The framework formalizes the process by which adaptive capacity erodes through increasing structural compression and declining response diversity. Unlike traditional resilience diagnostics that rely primarily on behavioral indicators such as variance or autocorrelation, the proposed approach operates at the level of structural constraints governing system responses. The framework introduces the Compression–Resonance–Tension Index (CRTI), defined as the ratio between adaptive resonance and structural compression. Structural compression is measured using conditional entropy to capture the degree to which system responses become historically constrained, while adaptive resonance quantifies the remaining diversity of responses under environmental stimuli. A complementary geometric measure, Response Manifold Entropy (Π), derived from the spectral entropy of response covariance matrices, characterizes the effective dimensionality of the system’s behavioral state space. Within this framework, systemic collapse is interpreted as the endpoint of a Singularization trajectory, a process in which the system’s response manifold collapses toward a single dominant behavioral mode. The framework hypothesizes that declining CRTI trajectories precede observable behavioral early-warning signals such as Critical Slowing Down (CSD). To test this hypothesis, the paper proposes an empirical validation design using patent citation networks in the hard disk drive (HDD) industry, applying entropy measures, spectral analysis, and survival models to evaluate whether structural deterioration precedes technological disruption. By integrating concepts from cybernetics (Ashby), ecological resilience theory (Holling), and information theory, the framework provides a unified diagnostic vocabulary for analyzing the failure mode of complex systems that emerges not from chaos, but from the elimination of adaptive variety. Keywords complex adaptive systems structural fragility information theory resilience diagnostics early warning signals critical slowing down entropy compression adaptive resonance CRTI singularization complex systems system collapse