$mathbb{1}$-Loop Theory

A new formalism for lattice gauge theory is developed that preserves Poincare symmetry in a discrete universe. We define the $mathbb{1}$-loop, a generalization of the Wilson loop that reformulates classical differential equations of motion as identity-valued multiplicative loops of Lie group elements of the form ${[g_1cdots g_n]=mathbb{1}}$. A lattice Poincare gauge theory of gravity is thus derived that employs a novel matter field construction and recovers Einsteins vacuum equations in the appropriate limit.