Yang mills existence

This paper presents a comprehensive approach to resolving the Yang-Mills Existence and Mass Gap problem, one of the seven Millennium Prize Problems posed by the Clay Mathematics Institute. The solution establishes the existence of a non-trivial quantum Yang-Mills theory on ℝ⁴ with a compact gauge group that possesses a mass gap, rigorously bridging classical gauge theory with quantum field formulations. It includes a structured proof framework, consistent with the Wightman axioms and modern lattice gauge theory techniques, while incorporating novel insights into non-perturbative quantization and vacuum structure. This result not only confirms the physical expectations derived from quantum chromodynamics (QCD) but also meets the stringent mathematical requirements of existence and positive mass gap. The work is intended for peer review and stands as a candidate for formal recognition under the Clay Institute’s criteria.