Here are some updates since the ArXIV submission.
  1. Typo in introduction "non-local mean distance" instead of "local mean distance".
  2. Top of page 14: Typo has the cluster coefficient 1000li> Classically, scalar curvature can be described by volumes of balls not volumes of spheres In the discrete, this does not matter. Since |B(x)| = 1+|S(x)| and |B_2(x)| = 1+|S(x)|+|S_2(x)| so that B_2/B_1 ~ 1+ |S_2|/|S_1| and averaging also just changes the Hilbert action by a constant.