  We study the behavior of holonomy spin foam partition functions, a form of
lattice gauge gravity, on generic 4d-triangulations using micro local analysis.
To do so we adapt tools from the renormalization theory of quantum field theory
on curved space times. This allows us, for the first time, to study the
partition function without taking any limits on the interior of the
triangulation.
  We establish that for many of the most widely used models the geometricity
constraints, which reduce the gauge theory to a geometric one, introduce strong
accidental curvature constraints. These limit the curvature around each
triangle of the triangulation to a finite set of values. We demonstrate how to
modify the partition function to avoid this problem. Finally the new methods
introduced provide a starting point for studying the regularization ambiguities
and renormalization of the partition function.
