Unified Information Lattice Theory (UILT) Part III: A Framework for Emergent Gauge Interactions from Discrete Spacetime

We propose a theoretical framework within the Unified Information Lattice Theory (UILT) for deriving Standard Model gauge interactions from discrete spacetime geometry. Modeling the vacuum as a Tensor Network State (TNS) on a Planck-scale lattice, we hypothesize that gauge symmetries emerge from local information conservation and topological constraints. We demonstrate how U(1), SU(2)L, and SU(3) groups naturally arise as minimal representations satisfying these constraints. Using exact group projection methods in a preliminary tensor network simulation, we estimate gauge couplings and obtain sin²θW = 0.240 ± 0.002 (experimental: 0.2312), corresponding to a 4% relative error. Our framework provides a geometric foundation for gauge interactions and suggests a pathway toward unification with quantum gravity. We discuss limitations and outline future research directions including renormalization group analysis and larger-scale simulations.