A Rigorous Mathematical Proof of the Yang-Mills Mass Gap via Fractal Corrections

One of the Millennium Prize Problems in mathematical physics is the proof of the massgap in non-Abelian Yang-Mills theory. This paper presents a rigorous proof that the lowesteigenvalue of the Yang-Mills Hamiltonian remains strictly positive, ensuring the existence ofa nonzero mass gap. Our proof introduces a novel fractal correction function, which stabilizesthe spectral structure of the gauge field operator. Using spectral analysis, the Rayleigh-Ritzmethod, and Schwinger-Dyson equations, we establish a strict lower bound on the mass gap.This work provides a fundamental mathematical solution to the non-perturbative problemof quantum gauge fields.