The Geometric Quantization of Interactive Systems: A Conditional Framework for Linear-Response Human-AI Dynamics

We propose a conditional mathematical framework for modeling interactive systems under coarse-grained, stable operating regimes. Discrete interaction loops are approximated by continuous dynamics via statistical averaging and linear response. When such systems admit an effective symplectic structure and are governed locally by quadratic Hamiltonians, canonical quantization yields coherent states that uniquely minimize uncertainty between conjugate interaction variables. We emphasize that this structure is neither universal nor robust: nonlinearities, dissipation, and optimization generically destroy coherence. The framework is explicitly local, falsifiable, and re- stricted to weak-feedback regimes.