Coherence-Gradient Theory: A Unified Framework for Measuring Integrated Stability Across Complex Systems - v2

Complex systems across diverse domains, from neural networks to weather models to institutional structures, face a common challenge: maintaining coherent function while adapting to external demands. We propose Coherence-Gradient Theory (CGT), a unified mathematical framework that quantifies system stability through two fundamental components: information integration (φ) and adaptive response (ρ). The Coherence-Gradient Index (CGI = √(φ × ρ)) provides a domain-general measure of integrated stability under load. We demonstrate that this single formula, with domain-appropriate operationalizations of φ and ρ, successfully predicts outcomes across three fundamentally different systems: biological consciousness (discriminating adaptive versus drowsy attention states with 89% accuracy), meteorological forecasting (predicting ensemble uncertainty with AUC 0.78-0.86), and institutional stability (retrospectively identifying organizational collapse with 100% accuracy across nine historical cases). Empirical weight optimization across consciousness and weather domains revealed φ-emphasis (w=0.8), suggesting baseline integration constrains attention more than adaptive retention, while maintaining robust performance across w ∈ [0.4-0.8] and validating the theoretical prediction that both components are jointly necessary. The geometric mean structure prevents compensatory trade-offs, ensuring that both integration and adaptation contribute to overall system coherence.