Canonical Geometry and Quantization of Effective Interactive Dynamics: A Conditional Structural Analysis

We construct a rigorous, conditional mathematical framework for describing the effective evolution of stable interactive systems. By modeling the coarse-grained in- teraction variables as coordinates on a finite-dimensional Kähler manifold ( M, ω, J, g), we derive the emergence of canonical commutation relations via geometric quantization. We prove that under the restriction to quadratic Hamiltonians, the stable eigenstates of the system are structurally equivalent to coherent states. Crucially, we delimit the theory by explicitly constructing failure boundaries—including dissipative gradient flows and non-quadratic regimes—where the symplectic structure collapses. Finally, we propose a set of empirically testable indicators based on linear response theory to verify the exis- tence of the postulated geometric structure in observational data. This work makes no ontological claims but establishes a falsifiable map between symplectic geometry and macroscopic interaction phenomenology.