  In the following work, we pedagogically develop 5-vector theory, an evolution
of scalar field theory that provides a stepping stone toward a
Poincar\'e-invariant lattice gauge theory. Defining a continuous flat
background via the four-dimensional Cartesian coordinates $\{x^a\}$, we `lift'
the generators of the Poincar\'e group so that they transform only the fields
existing upon $\{x^a\}$, and do not transform the background $\{x^a\}$ itself.
To facilitate this effort, we develop a non-unitary particle representation of
the Poincar\'e group, replacing the classical scalar field with a 5-vector
matter field. We further augment the vierbein into a new $5\times5$ f\"unfbein,
which `solders' the 5-vector field to $\{x^a\}$. In so doing, we form a new
intuition for the Poincar\'e symmetries of scalar field theory. This effort
recasts `spacetime data', stored in the derivatives of the scalar field, as
`matter field data', stored in the 5-vector field itself. We discuss the
physical implications of this `Poincar\'e lift', including the readmittance of
an absolute reference frame into relativistic field theory. In a companion
paper, we demonstrate that this theoretical development, here construed in a
continuous universe, enables the description of a discrete universe that
preserves the 10 infinitesimal Poincar\'e symmetries and their conservation
laws.
