AI Control Model v2.1: Generative Field Theory

AI Control Model v2.1: Generative Field Theory This work extends the AI Control Model series from localized internal dynamics to distributed generative fields. AI Control Model v1.0 established a tri-phase generative control grammar based on Dynamic, Static, and Breathing phases. AI Control Model v2.0 expanded this framework through multidimensional internal dynamics, oscillatory behavior, coupling structures, and stability envelopes. AI Control Model v2.1 introduces a generative field formulation in which the deep-state representation is extended from a localized state vector b(t) to a distributed state field b(x,t). The model incorporates four principal concepts: Spatial Embedding Field Coupling Purity Fields A Preliminary Background Field A continuous-time generative field equation is proposed together with a boundedness analysis under restricted assumptions. The framework is positioned as a theoretical extension of the AI Control Model series and as an intermediate step toward future Background Layer Control Theory. This release is intended as a theoretical research contribution and does not claim empirical validation. Experimental implementations and application studies are reserved for future work. Keywords: Generative Field Theory, AI Control Model, Tri-Phase Control, Deep State Dynamics, Field Coupling, Purity Field, Background Field, Generative Control