  The first computation of a spin foam dynamics that provides a test of the
quantum equations of motions of gravity is presented. Specifically, a
triangulation that includes an inner edge is treated. The computation leverages
the recently introduced effective spin foam models, which are particularly
numerically efficient. Previous work has raised the concern of a flatness
problem in spin foam dynamics, identifying the potential for the dynamics to
lead to flat geometries in the small $\hbar$ semiclassical limit. The numerical
results presented here expose a rich semiclassical regime, but one that must be
understood as an interplay between the various parameters of the spin foam
model. In particular, the scale of the triangulation, fixed by the areas of its
boundary triangles, the discreteness of the area spectrum, input from Loop
Quantum Gravity, and the curvature scales around the bulk triangles, all enter
the characterization of the semiclassical regime identified here. In addition
to these results on the dynamics, we show that the subtle nature of the
semiclassical regime is a generic feature of the path integral quantization of
systems with second class constraints.
