Jonathan,
You say, " ... it is necessary to assume that the geometry becomes both non-commutative and non-associative at that point. That is the gist of what Tevian primarily agreed with."
The geometry never becomes non-commutative or non-associative. That's impossible, because geometry (generalized to topology) is continuous. The properties are mathematical artifacts--the point I was making.
The least (only) representation of a complete algebra is the 2 dimensional complex plane, facilitating 4 dimension analysis -- and the least physically complete representation of 4 dimension geometry is the Minkowski space-time.
One gets a 16 point matrix from this artifact, 6 points of which are redundant with the 3-space coordinates of ordinary existence, leaving 10. So plenty of connections/relations available--with the constraint that the time parameter is included, not calculated out, nor normalized. This one extra degree of freedom compels the nonlinearity of the time metric (and accelerated relative motion) consistent with Einstein's observation that,
"The law of heat conduction is represented as a local relation (differential equation), which embraces all special cases of the conduction of heat. The temperature is here a simple example of the concept of field. This is a quantity (or a complex of quantities), which is a function of the co-ordinates and the time."
And the definition, also given by Einstein,
"I think of a quantum as a singularity, surrounded by a large vector field. With a large number of quanta a vector field can be composed that differs little from the one we presume for radiation."
All of which points to a complete field theory of quantum gravity--and by implication--to the origin of consciousness.
How does one account for the integrated role of time in your static model?