Hi Scott...
Mathematical physics that preserves "Scientific method" by providing visually verifiable kinematics, from what we empirically observe, to a single operative/mechanism underlying observation of Universal fundamental unification, "can offer a coherent 'assembly' of the evidence needed to advance understanding that already exists", REF: Richard Kingsley Nixey essay https://fqxi.org/community/forum/topic/3042, but it is doubtful that mathematics as semantics, which have been diluted to the exclusion of logic inference, are up to the task.
In that perception of motion requires Space, how can a point Spin without defining direction... i.e. direction is a Spatial property?
What differentiates "all the spinning point entities" from any one spinning point entity... i.e. location is a Spatial property?
How can mathematical relationships of spatially undefined entities... i.e. a point, spinning or otherwise... establish a mechanism/operative for Energy creation... i.e. can Energy emerge without a Spatial definition?
If Energy requires a Spatial definition, what mechanism provides impetus such that Space emerges from a conglomerate of spatially undefined differentiateable entities... i.e. density is a Spatial property?
What intelligence emerges such that "spinning point entities reorganized into a cubic lattice"... i.e. a lattice is an information framework.
A Digital SIM, animating pulsed distribution of unified minimum units of Energy (QE), within a CAD environment quantized by a 3D unified field single point Source encapsulation geometry... i.e. unified field empirical virtuality mechanix... is my computational analysis tool of choice for emergence and distribution/propagation analysis.
I have been unable to derive a "mathematical representation for the base energy state that is associated with spacetime ", but I have mathematically, specifically CAD/SIM visual geometry, derived a model that demonstrates "a base state"... i.e. Energy distribution equal in all directions from a single point... and visually verifies definition of unified/uniform minimum units of Space (QT) and unified/uniform minimum units of Energy (QE)... i.e. unified/uniform minimum unit implies scale invariance and no subsequent fraction of... associated with a Space/Energy model in which unified/uniform minimum units of Time and unified/uniform minimum units of Information are inherent.
The Unifed Quantization of a Singularity (UQS) coordinate math supports, by digital codec, derivation of Cartesian coordinate math, but it does not conversely insure "our current knowledge of physics" can be derived from Cartesian coordinate maths.
REF: Geometry Paradigms http://www.uqsmatrixmechanix.com/UQSReTB.php
REF: UQS Consciousness Investigation Geometry http://www.uqsmatrixmechanix.com/UQSConInv.php
Thanks Scott for sharing your insights, and your comments on my essay would be read with those insights in mind.
Sue Lingo
UQS Author/Logician
www.uqsmatrixmechanix.com