Structural Compression as a Mechanistic Driver of Entropy Collapse: The Compression–Resonance–Tension Index (CRTI) as a Diagnostic Complement to Critical Transition Theory

This paper introduces the Compression–Resonance–Tension Index (CRTI) as a dimensionless mechanistic diagnostic for systemic fragility in complex adaptive systems. CRTI is defined as T = R/Φ, where R denotes adaptive reorganization capacity and Φ structural compression. We propose that entropy collapse (Truong et al., 2025) can be reinterpreted as a phase transition driven by excessive structural compression, leading to the suppression of adaptive variance and the emergence of brittle attractors — a state termed Crystallization Death.By coupling CRTI dynamics within a bistable ODE framework, the paper shows that collapse is not merely a loss of entropy, but a transition into a high-order, low-resonance regime. This reframing provides a mechanistic bridge between entropy-based descriptions of adaptive failure and resilience theory, enabling quantification of systemic fragility and identification of collapse thresholds prior to bifurcation.The framework complements critical transitions theory (Scheffer, Dakos et al.) by offering a causal scalar operator whose temporal trajectory precedes conventional early warning signals (rising variance, critical slowing down). A three-zone diagnostic cascade (Yellow: Semantic Inbreeding → Orange: Structural Rigidity → Red: Resonance Muting) operationalizes the collapse trajectory for real-world monitoring.Applications are discussed for ecological systems (regime shifts, Peter Lake validation protocol), AI and machine learning (model collapse under recursive self-training), and economic and institutional systems (institutional sclerosis, organizational rigidity traps).This preprint is part of the Mallinckrodt Framework series. Related records: Master Paper (DOI: 10.5281/zenodo.18888415), Falsification Protocol (DOI: 10.5281/zenodo.19036931). critical transitions entropy collapse adaptive capacity structural compression bistable dynamics regime shift early warning signals resilience panarchy systemic fragility complex adaptive systems CRTI Compression-Resonance-Tension Index Mallinckrodt Framework tipping points crystallization death collapse threshold viability index dynamical systems phase transition