  The Riemann scalar curvature plays a central role in Einstein's geometric
theory of gravity. We describe a new geometric construction of this scalar
curvature invariant at an event (vertex) in a discrete spacetime geometry. This
allows one to constructively measure the scalar curvature using only clocks and
photons. Given recent interest in discrete pre-geometric models of quantum
gravity, we believe is it ever so important to reconstruct the curvature scalar
with respect to a finite number of communicating observers. This derivation
makes use of a new fundamental lattice cell built from elements inherited from
both the original simplicial (Delaunay) spacetime and its circumcentric dual
(Voronoi) lattice. The orthogonality properties between these two lattices
yield an expression for the vertex-based scalar curvature which is strikingly
similar to the corresponding hinge-based expression in Regge calculus (deficit
angle per unit Voronoi dual area). In particular, we show that the scalar
curvature is simply a vertex-based weighted average of deficits per weighted
average of dual areas.
