Gauge-Compatible Structures from ℓ¹ Defect Flows

This paper presents a constraint-based framework for the selection of gauge symmetry arising from ℓ¹ defect geometry on discrete structures. Starting from a minimal inconsistency functional, we impose a single structural principle: defect resolution must proceed via monotone reduction of local inconsistency. This induces a minimal cyclic closure (N = 3), whose transport operator forces complex phase structure and uniquely selects a unitary invariant metric. Within this framework, admissible symmetry groups acting irreducibly on the resulting state spaces are classified. The construction yields SU(3), SU(2), and U(1) as the unique symmetry structures compatible with minimal consistency, cyclic transport, and irreducibility constraints. The resulting gauge group SU(3) × SU(2) × U(1) emerges as a structural consequence of the framework, rather than from symmetry breaking of a larger unified group. The paper explicitly distinguishes between topologically robust results (group structure, generation count) and measure-dependent quantities (e.g., transport amplitudes), and does not assume a priori quantum mechanical structure. This work is part of a broader program investigating ℓ¹-based obstruction theory and its implications for physical and computational systems.