Universal Equation X(C) for Unified Gravitational and Quantum Dynamics: A New Framework for High-Energy Physics and Cosmology

In this paper, (in french sorry) 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. I provide a detailed mathematical derivation and empirical tests of the equation, demonstrating its ability to regularize divergences in general relativity and incorporate quantum corrections. The equation's validity is assessed through several test cases, including the evaporation of Planck-scale black holes, where the results align with theoretical expectations. This work highlights the potential of X(C)to provide a comprehensive, self-consistent description of space-time dynamics, offering a new tool for researchers in high-energy physics and cosmology.