  We introduce the construction of a new framework for probing discrete
emergent geometry and boundary-boundary observables based on a fundamentally
a-dimensional underlying network structure. Using a gravitationally motivated
action with Forman weighted combinatorial curvatures and simplicial volumes
relying on a decomposition of an abstract simplicial complex into realized
embeddings of proper skeletons, we demonstrate properties such as a minimal
volume-scale cutoff, the necessity of a positive-definite cosmological
constant-like term as a regulator for non-degenerate geometries, and naturally
emergent simplicial structures from Metropolis network evolution simulations
with no restrictions on attachment rules or regular building blocks. We see
emergent properties which echo results from both the spinfoam formalism and
causal dynamical triangulations in quantum gravity, and provide analytical and
numerical results to support the analogy. We conclude with a summary of open
questions and intent for future work in developing the program.
