Topological Friction and the Yang-Mills Mass Gap: A Dynamical Resolution via the Hernández-Valdivia Limit

The Yang-Mills Mass Gap (∆ > 0) remains one of the most profound unsolved problems in theoretical physics, pri-marily because continuous non-Abelian gauge theories struggle to analytically describe infrared confinement withoutad-hoc mechanisms. In this paper, we apply the Theory of Finite Systems to Quantum Chromodynamics (QCD).We propose that the mass of glueballs and confined hadrons is not generated by a spontaneous symmetry-breakingscalar field, but emerges as a macroscopic manifestation of “topological friction” within the discrete Ramanujanmodular lattice. By introducing the Hernández-Valdivia Limit (ϵHV ) into the Yang-Mills Lagrangian as a higher-derivative gauge-covariant dissipation term, we mathematically demonstrate that massless gluons cannot propagateto infinity. Instead, they hit a geometric bandwidth limit, converting kinetic energy into inertial mass and enforcingcolor confinement.