A Dynamical Background Field in Kaluza-Klein Theory: A Formal Framework for Stability and Resonance in Higher-Dimensional Spacetimes

We propose a formal extension of the 5D Kaluza-Klein formalism by introducing a dynamic, classical scalar field Ψ propagating in the compactified dimension. This field couples to the higher-dimensional geometry and gives rise to an effective 4D theory featuring a derived, dynamic existence coefficient d. This coefficient, a function of the background field's energy density, parametrizes the stability of the compactification. We demonstrate that the model naturally leads to an ontological tension T(d) that drives the system toward higher-stability configurations. The framework suggests novel, testable implications for the cosmological constant problem and the stability of fundamental constants. This work provides a purely geometric and field-theoretic foundation for discussing stability hierarchies in higher-dimensional physics.