AI Control Model v2.0: Internal Dynamics Expansion of a Tri-Phase Generative Control Framework

AI Control Model v2.0 extends the foundational tri-phase generative control framework introduced in v1.0 by formalizing the internal dynamical structure of the deep-state vector b(t). The model introduces multi-component deep-state dynamics, internal oscillatory modes, cross-phase coupling operators, and a stability envelope for amplitude regulation. This version establishes a mathematical framework for analyzing internal generative dynamics and provides representative operator formulations, Jacobian analysis, parameter examples, and simulation code. The framework expands the original tri-phase architecture by incorporating dynamic interactions among internal state components and phase-dependent modulation mechanisms. AI Control Model v2.0 serves as a bridge between the foundational Tri-Phase Generative Control Framework presented in v1.0 and future developments involving spatial embedding and field-theoretic extensions planned for v2.1. Contents: • Tri-Phase Generative Structure • Multi-Component Deep-State Vector • Internal Oscillatory Mode System • Dynamic, Static, Breathing, and Coupling Operators • Stability Envelope Formulation • Composite Update Equation • Jacobian Analysis • Numerical Example • Python Simulation Code Author: Akio Nomura ORCID: 0009-0000-8270-1713 Affiliation: Independent Researcher License: Creative Commons Attribution 4.0 International (CC BY 4.0) Keywords: AI Control Model, Tri-Phase Model, Generative Control, Deep-State Dynamics, Oscillatory Systems, Stability Envelope, Mathematical Modeling, Artificial Intelligence