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

**Abstract:** This paper presents a structural derivation of gauge symmetry from the discrete angular coherence dynamics of triadically spinning units in the Holosphere lattice. Instead of imposing U(1), SU(2), and SU(3) as abstract internal symmetries, Holosphere Theory reconstructs them from physical constraints on angular phase closure, coherence role switching, and orbital permutations within a real-valued, rotating lattice. Gauge fields are reinterpreted as angular strain gradients rather than mathematical compensators, and force carriers emerge as coherence reconfiguration packets. The Triplet Charge Closure Condition provides the foundation for charge quantization, while directional coherence constraints lead to testable predictions such as quantized coupling thresholds, directional weak decay anisotropies, and lattice-governed confinement behavior. This paper completes the triadic spin symmetry series (T1–T5) and prepares the foundation for Holosphere QCD in Papers 52, 53, and 55.