  Canonical quantum theories with discrete space may imply interesting effects.
This article presents a general effective description, paying due attention to
the role of higher spatial derivatives in a local expansion and differences to
higher time derivatives. In a concrete set of models, it is shown that spatial
derivatives one order higher than the classical one are strongly restricted in
spherically symmetric effective loop quantum gravity. Moreover, radial holonomy
corrections cannot be anomaly-free to this order.
