Emergence of Gauge Symmetries and Bell Correlations from a Discrete Ternary Lattice

Abstract Current attempts to unify General Relativity and Quantum Mechanics are hindered by the "Continuity Problem"—the mathematical incompatibility between the smooth spacetime of relativity and the discrete quanta of particle physics. This paper presents a model by deriving the continuous Lie Group symmetries of the Standard Model as the continuum limit of a discrete ternary manifold (UIT-81). We demonstrate that the degrees of freedom in a 3 3 ternary grid form a closed Lie Algebra structurally isomorphic to the SU(3) generators, provided the imaginary unit i is defined not as a scalar, but as a discrete symplectic operator Sab representing cyclic planar rotation. By applying the Trotter-Suzuki product formula to the sequential activation of grid states, we prove that the discrete step-functions of the ternary voxel converge exactly to the smooth Unitary Evolution operators of Quantum Field Theory (U(t) =e-iHt) in the limit of vanishing grid spacing (a 0). Finally, we calculate the CHSH correlation for the grid, deriving the Tsirelson bound of. . This confirms that the non-commutative geometry of the ternary buffer reproduces quantum non-locality and entanglement entropy as emergent properties of a deterministic integer-based architecture.