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The following work demonstrates the viability of Poincar\'e symmetry in adiscrete universe. We develop the technology of the discrete principalPoincar\'e bundle to describe the pairing of (1) a hypercubic lattice `basemanifold' labeled by integer vertices-denoted$\{\mathbf{n}\}=\{(n_t,n_x,n_y,n_z)\}$-with (2) a Poincar\'e structure group.We develop lattice 5-vector theory, which describes a non-unitaryrepresentation of the Poincar\'e group whose dynamics and gauge transformationson the lattice closely resemble those of a scalar field in spacetime. Wedemonstrate that such a theory generates discrete dynamics with the completeinfinitesimal symmetry-and associated invariants-of the Poincar\'e group.Following our companion paper, we `lift' the Poincar\'e gauge symmetries to actonly on vertical matter and solder fields, and recast `spacetime data'--storedin the $\partial_\mu\phi(x)$ kinetic terms of a free scalar field theory--as`matter field data'-stored in the $\phi^\mu[\mathbf{n}]$ components of the5-vector field itself. We gauge 5-vector theory to describe a lattice gaugetheory of gravity, and discuss the physical implications of a discrete,Poincar\'e-invariant theory.

Restoring Poincar\'e Symmetry to the Lattice