  Three-dimensional gravity coupled to pressureless dust is a field theory with
one local degree of freedom. In the canonical framework, the dust-time gauge
encodes this physical degree of freedom as a metric function. We find that the
dynamics of this field, up to spatial diffeomorphism flow, is independent of
spatial derivatives and is therefore ultralocal. We also derive the linearized
equations about flat spacetime, and show that the physical degree of freedom
may be viewed as either a traceless or a transverse mode.
