  The relational framework of canonical quantum gravity with non-ultralocal
constraints is explored. After demonstrating the absence of anomalies, a
spatially discretized version of the relational framework is introduced. This
allows the application of Lieb-Robinson bounds to on-shell monotonic gauge-flow
when there is a continuous external "time" parameter. An explicit Lieb-Robinson
bound is derived for the differential on-shell evolution of the operator norm
of the commutator of discretized Dirac observables, demonstrating how a local
light cone-like causal structure emerges. Ultra-local constraints do not permit
such a structure to arise via Lieb-Robinson bounds. Gauge and (3+1)-diff
invariance of the light-cone is discussed along with the issues of quantum
fluctuations, the nature of the non-localities, the spatial continuum limit,
and possible links to non-commutative geometry.
