Paper T5: Triadic Field Symmetries and Gauge Structure in Holosphere Theory

We investigate the origin of gauge symmetries in quantum field theory from the perspective of Holosphere Theory, a discrete, coherence-based model of spacetime built from triadically spinning, nested lattice units. Unlike standard quantum field theory, where internal symmetry groups such as U(1), SU(2), and SU(3) are imposed axiomatically, Holosphere Theory derives these structures from the physical dynamics of triadic angular coherence. We show that the Triplet Charge Closure Condition imposes strict rotational phase constraints that give rise to real-valued analogs of electromagnetic, weak, and strong gauge symmetries. The U(1) symmetry emerges from continuous angular phase preservation within a single triplet orbital. SU(2)-like behavior arises from binary coherence branchings between dark bosons and lattice defects, while SU(3) emerges from permutation symmetries among the three axes of triadic spin. Gauge invariance is interpreted as the preservation of coherence under local phase reconfiguration, with force mediators corresponding to discrete coherence rebalancing events. This structural interpretation offers a falsifiable, geometric alternative to standard model gauge theory [4] and lays the foundation for a coherence-based unification of forces in future Holosphere QCD models.