CRTI 2.0: A Bias-Corrected Information-Theoretic Ratio for Quantifying Rigidity–Permeability Trade-offs in Adaptive Networks

This preprint presents CRTI 2.0 (Compression–Resilience Tension Index), a stabilized and bias-corrected information-theoretic ratio for quantifying the relationship between structural redundancy and environmental information integration in adaptive networks. The framework defines structural rigidity as normalized transition entropy reduction and feedback permeability as normalized mutual information between environmental input and system output. To ensure numerical stability in low-coupling regimes, a window-derived regularization parameter (ε = 1/W) is introduced, yielding the stabilized ratio: Tε = R / (Φ + ε) All entropy and mutual information estimates employ Miller–Madow bias correction to address finite-sample effects. The methodology is validated using an agent-based adaptive Markov network with Monte Carlo simulations (≥200 runs per condition), system size scaling (N ∈ {50, 100, 500}), environmental entropy variation, and feedback delay analysis. Collapse detection is operationalized via Critical Slowing Down indicators (variance increase, lag-1 autocorrelation increase, and fitness derivative). Statistical robustness is assessed using bootstrap confidence intervals (B=1000) and permutation testing (B=2000). Predictive performance is evaluated via AUC and Brier Score. This preprint documents the formal definition, simulation architecture, parameter freeze configuration, and statistical validation procedures. The contribution is strictly methodological and confined to measurable information-theoretic properties of adaptive systems. Code and reproducibility materials are provided in the associated repository. Information Theory Mutual Information Entropy Estimation Miller–Madow Bias Correction Transfer Entropy Complex Adaptive Systems Network Dynamics Phase Transition Detection Critical Slowing Down Early Warning Signals Adaptive Networks Structural Redundancy Information Integration Monte Carlo Simulation Systemic Rigidity