Singular Attractor Decomposition and Vorton Dipole Superposition in 3d Navier–stokes and Classical Yang–mills Equations

Apparent finite-time singularities and topological reconnections in three-dimensional incompressible Navier–Stokes and classical Yang–Mills equations represent the weak convergence of continuous fields onto an exact, finite-dimensional dynamical attractor. Grounded in Walter Rudin's functional analysis theorems on distribution limits, smooth velocity and chromomagnetic fields contracting under strain collapse into a discrete superposition of solenoidal vorton dipoles rather than diverging to unphysical infinities. This decomposition reduces the continuous partial differential equations to an autonomous system of interacting ordinary differential equations that tracks vorton positions, circulation dipole moments, and non-Abelian color charges while preserving hydrodynamic impulse invariants. Filament crossings and reconnections proceed continuously through the Aksman–Novikov vertex, shifting topological linking numbers by integer steps without kinetic velocity blow-up. Because intense enstrophy is geometrically confined to one-dimensional vortex filament skeletons rather than volume-filling regions, the attractor's phase-space dimension scales with the three-fourths power of the Reynolds number rather than the classical nine-fourths power. Matching the finite vorton core radius to the Kolmogorov dissipation scale establishes an exact physical cutoff, precluding sub-Kolmogorov breakdown in fluids and regularizing non-Abelian chromomagnetic cascades through color viscosity.