CRTI 2.1: Consolidated Statistical Verification Framework for Detecting Structural Overcompression in Complex Adaptive Systems

CRTI 2.1 – Consolidated Statistical Verification Framework for Detecting Structural Overcompression in Complex Adaptive Systems Abstract CRTI 2.1 (Compression–Resonance Tension Index) is a nonlinear, information-theoretic diagnostic framework designed to detect structural overcompression in complex adaptive systems. It operationalizes the hypothesis that systemic fragility emerges not from disorder, but from excessive constraint accumulation that suppresses adaptive variety (“ordered fragility”). The framework defines structural rigidity as the entropy-reduction rate imposed on a system’s admissible state space and relates it to channel-specific processing capacity. The effective system tension T_{eff} integrates both linear channel contributions and nonlinear inter-channel coupling effects. This consolidated release formalizes the statistical verification architecture required to transform CRTI from a conceptual model into a falsifiable diagnostic instrument. It includes: Jackknife entropy estimation to mitigate finite-sample bias N/k monitoring for sampling-density validation State-Space Reduction Protocol (SSRP) using NMI-based redundancy collapse Stationarity Detection Protocol (SDP) based on Jensen–Shannon divergence and Page–Hinkley change detection Explicit window-rejection criteria under non-stationarity Formal falsifiability conditions CRTI 2.1 explicitly defines conditions under which diagnostic output is withheld, thereby enforcing epistemic discipline and preventing “ghost-order” artifacts caused by telemetry collapse or sparse sampling. The framework is currently in Pre-Empirical Validation Phase, pending controlled stress-to-failure calibration experiments in modular technical systems. Development History (Version Evolution) CRTI 1.0 Initial scalar diagnostic ratio linking structural rigidity to processing capacity. Conceptual articulation of “ordered fragility” and the overcompression hypothesis. CRTI 2.0 Channelized formulation introducing multi-dimensional tension components and bias-corrected aggregation. Recognition of selective resonance and cross-domain comparability challenges. CRTI 2.1 Nonlinear coupled formulation: Quadratic inter-channel interaction term Formal information-theoretic definition of structural rigidity Boundary & Measurement Protocol (Maximum Observable Variety) State-Space Reduction Protocol (SSRP) Jackknife entropy estimator integration Stationarity Detection Protocol (SDP) Explicit falsifiability and data-quality rejection criteria CRTI 2.1 represents the transition from theoretical framework to statistically disciplined diagnostic instrument architecture. 15 Scientifically Optimized Keywords Complex Adaptive Systems Information Theory Shannon Entropy Structural Overcompression Ordered Fragility Nonlinear Dynamics Jensen–Shannon Divergence Jackknife Estimation Mutual Information Change-Point Detection Cybernetics Systems Diagnostics State-Space Reduction Early Warning Systems Adaptive Capacity