Universal Scalar Equation X(C): A Minimal Framework for Unifying Classical and Quantum Gravitational Dynamics

In this paper, I propose a universal scalar equation X(C), designed to unify classical, quantum, and geometric effects across various physical contexts. The equation is constructed using a single scaling parameter κ\kappaκ, and applies to high-energy physics, cosmology, and gravitational dynamics. The proposed formulation aims to bridge the gap between general relativity and quantum mechanics, offering a consistent framework for modeling extreme phenomena such as black holes, gravitational waves, and early universe conditions. A detailed mathematical derivation and a series of empirical tests demonstrate the equation’s ability to regularize divergences in general relativity and incorporate quantum corrections. The equation's validity is assessed through multiple test cases, including the evaporation of Planck-scale black holes, with results aligning with theoretical expectations. This work highlights the potential of X(C) to offer a comprehensive, self-consistent description of space-time dynamics and to serve as a practical tool for researchers in high-energy physics and cosmology.