Dear Ray,
I enjoyed your essay and understand a few of your points better than before.
As I mentioned to Lawrence elsewhere, while I agree with you that "a physical infinity cannot exist within our Observable Universe", it certainly appears that infinite numbers of math formulas, relationships, solutions and structures can exist in the 'representational' universe.
Should a Theory of Everything focus on the infinite representations, attempting to produce "the one" universe, represented as the sum of some finite combination of representations, or attempt to begin with 'one' universe, the simplest possible, and physically evolve the universe we know today. Some of these essays appear to wish to accomplish this with a photon (a single photon?), some with a qubit (or two or four qubits). I wish to do so with a single field, the field of gravity.
The gravity field begins with perfect symmetry. A quantum of action implies that this symmetry can break, and a circulational aspect of the field come into existence, in addition to the original radial field. This circulation leads to vortices that can reach a limit (implied by the speed of light) and new Calabi-Yau curved structure come into existence-- particles.
These physical vortices are bosons, producing physical effects--fermions-- 4D stable Calabi-Yau structures... stable, that is, unless sufficient energy 'unwinds' them into a new vortex (boson).
'Struts' (reciprocal lattice vectors) that connect the direct lattice vertices "represent bosons", but it is mathematical, not a physical representation.
In this sense our approaches are 'reciprocal' or 'inverse'. In trying to find the simplest physical theory of our universe, I judge my success by the number of physics anomalies that aren't anomalous in my theory, regardless of representations. You seem to be trying to find the simplest mathematical representation of our universe without worrying about how bosons physically "produce" fermions (or vice versa).
Vortex bosons as physically real field phenomena lead to the particles and generations of particles that we have. Vortices of a left-handed C-field can only produce left-handed neutrinos. There are not, and will not be, right handed neutrinos, whereas SUSY, I believe, expects three right-handed neutrinos to explain the mass of the left-handed neutrino.
Your version of bosons, while not physically explaining how they work, represent connections between vertices (particles) and may be useful for predicting undiscovered particles.
A few more years of LHC operation should reward one of our approaches.
Yours is an impressive approach. You make many things fit together.
Edwin Eugene Klingman