Volume II — Mathematical and Probabilistic Theory of Governability : Toward a Unified Formalization of Memory, Observability, Saturation, and Regime Transitions in Complex Adaptive Systems

This volume develops the mathematical, probabilistic, and computational foundations of a general theory of governability for complex adaptive systems. Building upon the conceptual framework established in Volume I, it formalizes memory, observability, accumulation, saturation, conditional reversibility, and regime transitions within a unified mathematical architecture. The work introduces axioms, state spaces, probabilistic inference mechanisms, operators, metrics, and computational models designed to characterize complex system dynamics. Particular attention is given to latent states, path dependence, endogenous constraints, and critical thresholds. The framework seeks to transform governability into a formalizable, measurable, and testable quantity. Mathematical correspondences are established among the CBD, MOST, UCQ, DUAL, ECA, and RAG-RES frameworks. The objective is not deterministic prediction but the rigorous analysis of stability, adaptation, resilience, and systemic transformation. Together with Volume I, this work contributes to the development of a general science of governability for complex adaptive systems.