Classical Mass Transmutation in Yang–Mills Theory via Borromean Solitons and the Faddeev–Niemi Knot Ansatz

Derrick's Scaling Resolution: Classical Yang-Mills fields typically cannot form stable static solitons because smooth field configurations either collapse conformally to a singular point or disperse to infinity. Two-Sided Geometric Barrier: Decomposing the gauge fields into Borromean chromo-magnetic flux tubes creates a two-sided scale obstruction. Short-distance collapse is halted by an infinite enstrophy barrier that forbids flux-line crossing under ideal circulation transport, while long-distance dispersal is blocked by linear flux-tube tension. Classical Mass Transmutation: Balancing core enstrophy repulsion against long-range string tension yields a unique, stable energy minimum at a finite radius, generating a localized rest mass without quantum loop corrections or scalar Higgs fields. QCD Phenomenology: Because the three flux loops are pairwise unlinked, they move freely at short distances, mirroring asymptotic freedom. Because they are collectively inseparable through a non-vanishing triple-commutator invariant, isolated two-body states cannot exist, reproducing the three-body confinement logic of color gauge theory. Vorton Correspondence: In the thin-core limit, these knotted configurations map directly to discrete solenoidal vorton dipoles, establishing that classical mass generation is an intrinsic geometric consequence of non-Abelian vortex dynamics.