Primordial Yang-Mills Non-Abelian Vorticity Turbulence, Faddeev-Niemi Geometry, Borromean Solitons, and Natural Mass Gap Transmutation

Topological Field Decomposition: Decomposes the non-Abelian gauge connection using the Cho-Faddeev-Niemi representation into an Abelian background and a topological color unit vector. This structure isolates stable, localized chromomagnetic knot solitons classified by an integer topological Hopf invariant. Non-Linear Turbulence & Self-Limiting Saturation: Non-Abelian self-interactions drive a strongly non-linear gauge enstrophy cascade that proliferates flux tubes across scales. This cascade terminates deterministically at a close-packing limit governed by dimensional transmutation, where core-to-core repulsion extinguishes further vortex stretching and freezes the network into stable solitons. Borromean Confinement & Standard Model Geometry: The saturated network condenses into three-loop Borromean links. Because any two loops are pairwise unlinked, constituent fields interact weakly at short range (asymptotic freedom); however, their inseparable collective triple linkage prevents isolating any single loop without generating an infinite-energy flux tube (topological color confinement). Permutations of the three loops generate color symmetry, ribbon twist and writhe framing generate weak isospin, and longitudinal phase circulation generates hypercharge. Dynamical Mass Gap: Applying the Vakulenko-Kapitansky topological energy bound prevents the knotted chromomagnetic flux tubes from shrinking to zero size. This establishes an absolute, strictly positive lower energy floor for any localized excitation above the vacuum, resolving the non-perturbative Yang-Mills mass gap and deriving the scalar glueball ground state.