  This article is an extended version of the peer-reviewed publication; Moffat
and Wang, J Phys Math 2018, 9:4 DOI: 10.4172/2090-0902.1000289 The article sets
out to address a number of issues concerning Loop Quantum Gravity raised by
Ashtekar, such as in a recent post to Arxiv.org (A Ashtekar Arxiv:gr-qc
/0702030 v 2.0 May 2007). These include, for example, conditions for the
existence of Poincare invariant quantum states. In doing so, this article
provides a coherent mathematical framework for both the evolution of space-time
and the supersymmetric graviton in the early universe. In this extended form,
it is mnhopefully more accessible to research students at the advanced
undergraduate level and beginning doctoral level. The key extensions are: a. An
explicit cohomology based link between movement across a computational spin
network and a dimensioned embedding of the network to produce equivalent
movement along a discrete path in space-time; b). A discussion of the
implications for quantum ergodic theory and black hole dynamics.
