Comprehensive Integrated Theory of Casino Protocol: Integration of Yin-Yang Multiplicative Model, Hierarchical AI Architecture, and Deterministic Governance

Abstract This paper presents a comprehensive foundational theory formalizing Eastern "Yin-Yang" complementarity as multiplicative equilibrium to overcome polarization, systemic exploitation, and context collapse in artificial intelligence and social governance. The evaluation function P = 2500(1 - d^2) is formulated not merely as a geometric index, but as a top-level governance principle designed to detect and correct exploitative structural imbalances. We structure our framework into three distinct tiers: (1) Mathematical Theorems & Upper Governance Norms, (2) Engineering Design via a 3-layer architecture and 3C³ oracle, and (3) Empirical Hypotheses. Based on the harmonic mean T of 3C³, a deterministic access control gate G is engineered to regulate participation eligibility and resource access to the upper system without terminating the independent lower-layer LLMs.