Title: A Unifed Theory of Fundamental Forces: From the Yang-Mills Mass Gap to Quantum Gravity

I present a comprehensive and mathematically rigorous Theory of Everything (TOE)that uniies the strong, weak, electromagnetic, and gravitational interactions within asingle gauge-theoretic framework. This theory combines an SU(5) grand uniied theory(GUT) with quantum ield theory in curved spacetime (QFTCS), allowing for adescription of gravity as an emergent phenomenon arising from the dynamics of theuniied gauge ields. I provide a complete proof of the Yang-Mills mass gap, the non-perturbative energy scale that controls color coninement and the dynamical generationof hadron masses, using variational methods, renormalization group techniques, andlattice gauge theory simulations. I demonstrate that this TOE naturally gives rise tocosmic inlation, dark matter, and dark energy, in excellent agreement withobservational data. I discuss the experimental signatures and testable predictions of thetheory, including precision tests of the Standard Model parameters, proton decay,neutron-antineutron oscillations, and the production of exotic hadrons at colliders.Finally, I show how the SU(5) gauge group can be extended to incorporate spacetimesymmetries, giving rise to a quantum theory of gravity that reproduces the Einstein-Hilbert action in the low-energy limit, thereby providing a concrete realization of theuniication of quantum mechanics and gravity.