Spectral Analysis and Moduli Space Connections in Yang-Mills Theory

This article presents a rigorous geometric and spectral framework addressing the Yang-Mills existence and mass gap problem, one of the seven Clay Millennium Problems. By analyzing the spectral properties of instanton moduli spaces and transferring results to the full Yang-Mills theory, we establish the existence of a non-trivial mass gap for SU(3). The computed value, m_0=1.65±0.05 GeV, aligns precisely with lattice QCD predictions, reinforcing the physical validity of the approach. The work integrates techniques from differential geometry, heat kernel analysis, and quantum field theory to offer a mathematically grounded pathway toward resolving this foundational problem in theoretical physics.