Classical Resolution of the Yang–Mills Mass Gap: Virial Balance, Parabolic Gradient Flows, Color Viscosity, and Borromean Vorton Duality

In temporal gauge, classical non-Abelian gauge fields map directly to three-dimensional fluid mechanics, where spatial gauge connections act as fluid velocity and chromomagnetic curvature corresponds to physical vorticity. Non-linear self-interactions generate convective vortex stretching, driving a forward enstrophy cascade that transfers energy to smaller scales and prevents the existence of static, gapless infrared waves. Coarse-graining unresolved subgrid fluctuations produces an emergent color transport viscosity. The forward cascade terminates at an intrinsic dissipation microscale that identically matches the geometric threshold where spatial field gradients balance non-Abelian commutators, establishing a finite, non-zero vorton core radius from pure classical dynamics. Stationary precessional rotation generates an outward chromoelectric centrifugal pressure that balances inward chromomagnetic line tension, establishing a stable virial equilibrium that circumvents classical collapse theorems. In three-color gauge theory, closed flux tubes assemble into a Borromean triad whose global entanglement is protected by an invariant triple linking topology even though all pairwise linking vanishes. Because non-zero vortex cores cannot pass through one another without triggering reconnection, threading two flux tubes through the interior hole of a third ring imposes an irreducible geometric minimum on the aperture size and total loop perimeter. Multiplying this minimal topological length by the non-zero tube line tension bounds the total rest energy strictly away from zero, establishing an absolute positive mass gap as an emergent consequence of classical non-linear fluid geometry.