EXISTENCE OF THE MASS GAP: Discrete Vacuum Stabilization in Yang-Mills Theory via Pezzotti Metric

Following the successful application of the "Pezzotti Discrete Saturation Method" to Complexity Theory and Fluid Dynamics, this paper addresses the fifth Clay Millennium Problem: Yang-Mills and the Mass Gap.I demonstrate that in a quantized spacetime lattice, the vacuum energy state cannot collapse to zero. A strictly positive lower bound (\Delta > 0), known as the Mass Gap, is structurally enforced by geometric phase saturation. The massless state is algebraically forbidden in this framework.在佩佐蒂离散饱和法（Pezzotti Discrete Saturation Method）成功应用于复杂性理论与流体动力学领域后，本文聚焦于克莱数学研究所千禧年大奖难题（Clay Millennium Problem）的第五题：杨-米尔斯（Yang-Mills）与质量间隙（Mass Gap）。本文证明：在量子化时空晶格中，真空能量态无法坍缩至零。由几何相位饱和在结构上强制要求的严格正下界（Δ>0）即所谓的质量间隙。在此研究框架下，无质量态在代数层面上被禁止存在。