Emergence of Non-Abelian Gauge Structures from Topological Torsion in a Coercive Vacuum Field.

We extend the TUO–NS operator-theoretic framework to internal symmetry multiplets and non-Abelian gauge structures. Building on the emergence of conserved Abelian charges from topological torsion, we argue that once the internal configuration space of a coercive vacuum admits multiple interacting torsional directions, admissible configurations can organize into effectively non-commuting charge generators, under physically motivated assumptions of locality, coercivity, and finite-energy localization. We show that non-Abelian gauge redundancy arises as a representational necessity when distinct torsional windings cannot be simultaneously trivialized by admissible homotopies. Gauge connections and curvature tensors emerge as long-wavelength bookkeeping devices encoding path-dependent transport in internal configuration space. Quantization of multiplet structure follows from topological admissibility and energetic isolation of composite torsional states, without invoking any a priori group axioms or canonical quantization. Within this framework, the mathematical backbone of non-Abelian gauge theories appears as a structural consequence of vacuum coercivity and topological obstruction, rather than as a fundamental symmetry postulate.