[CD-PMS-03] Running Coupling and β-Function in Unified Constraint Dynamics: A General Field Theory of Meaning Space

This paper is part of the research series Constraint Dynamics in Parametrized Markov Systems. The series investigates structural constraints governingexploration dynamics in parametrized Markov systems. Core themes include: • operator distinguishability collapse• Fisher information geometry• exploration constraint mechanisms• collapse boundaries• quadratic Fisher scaling Series index CD-PMS-01 Three Collapse Boundaries in Finite-State Systems with DAG Structure and FrictionCD-PMS-02 Gaussian Curvature of Two-Parameter Exponential Families on Finite State Spaces with Application to Constrained Markov SystemsCD-PMS-03 Three Collapse Boundaries in Parametrized Markov Systems