The Effective Theory of QWIM: A Stochastic-Bayesian Derivation of Two-Phase Decision Dynamics

Version 4.5 provides a rigorous mathematical foundation for the QWIM model, formulated as an effective theory. Unlike previous numerical frameworks, this version introduces a formal derivation of the Fokker-Planck equation for decision landscapes and establishes a direct connection to Variational Bayesian Inference and the Free Energy Principle (FEP). Key highlights: (1) Analytical proof of the stochastic-to-dissipative transition, (2) Definition of thermodynamic costs via stochastic entropy production, and (3) Optimization of decision speed via stochastic resonance. This document represents the definitive mathematical formulation of two-phase decision dynamics. This project is now under legal monitoring. All commercial implementations must contact the author.