EXACT YANG–MILLS SPECTRAL MASS GAP FROM NON-ABELIAN KOLMOGOROV MICROSCALE AND SOLENOIDAL VORTON DYNAMICS

This treatise resolves the classical Yang–Mills mass gap dilemma by proving that scale invariance is broken dynamically at the classical continuum level through kinematic color viscosity, eliminating the need to smuggle in quantum mechanics or Planck's constant. In a dense non-Abelian color medium, viscous dissipation halts the turbulent wave cascade at an exact classical Kolmogorov microscale, where non-linear convective turnover balances color diffusion. At this termination boundary, the continuous gauge field condenses into an ensemble of localized solenoidal vorton defects. The defect core diameter is selected autonomously by balancing flow straining against color diffusion, avoiding circular parameter definitions. Formulating these fields through the double curl of a smooth vector potential guarantees that both velocity and chromomagnetic fields remain strictly divergence-free across all space without delta-function singularities. Linear perturbations propagating through the condensed vorton lattice encounter an invariant classical spectral cutoff frequency. Modes below this threshold are strictly evanescent in the bulk, producing exponential spatial Yukawa screening. The classical kinetic energy per unit length of an isolated flux tube acts as an exact mechanical string tension, which proves the Wilson loop area law of confinement through the Poisson statistics of independent vortex piercings. Finally, using Planck's constant strictly as a dimensional unit conversion translates this classical cutoff frequency into the observed scalar glueball mass scale, establishing infrared confinement and mass generation from first principles.