Paper T1: Triadic Angular Quantization in the Holosphere Lattice

In Holosphere Theory, the universe is modeled as a discrete lattice of rotating Holospheres, each composed of nested Planck-scale spheres aligned in cuboctahedral symmetry. This paper introduces the concept of triadic angular quantization, demonstrating that angular coherence within this structure supports only three stable rotational phase states separated by 120◦. We derive a real-valued coherence model in which spin, quantization, and orbital behavior emerge from discrete angular strain energy rather than from continuous symmetries or complex-valued wavefunctions. The triadic rotation operator R120 replaces the imaginary unit as the generator of phase dynamics, leading to a three-state coherence system that underlies particle spin, phase propagation, and orbital identity. This work establishes a mathematical and geometric basis for angular quantization in the Holosphere lattice and sets the stage for subsequent developments in real-valued quantum mechanics, particle generation, and gauge field emergence from triadic coherence.