Topological Resolution of the Yang-Mills Mass Gap: An Approach via Quantized Relational Dynamics Lattice Rigidity (PR-TAU 5.2.1)

One of the major challenges in mathematical physics is to prove the existence of a "Mass Gap" ($\Delta > 0$) in Yang-Mills theories. In this paper, we propose a solution based on the \textbf{PR-TAU 5.2.1} protocol, where the vacuum is treated as a topological solid endowed with intrinsic rigidity. We demonstrate that the mass of gauge states is not a fundamental property, but rather a deformation energy of the QRD lattice imposed by an angular closure defect $\epsilonTAS \approx 0.000576$. This model explains quark confinement and predicts proton stability by linking nuclear critical pressure to the mass gap.