"So there are connections with some established physics here."
The things you are talking about here, Fano planes and Jacobi functions, are things that some of my correspondents also talk about. In particular, Michael Rios see math-ph/0503015. Marni Sheppeard in her blog:
http://kea-monad.blogspot.com/2007/08/m-theory-lesson-80.html
talks about Fano planes and references a blog post of mine which link is out of date. To see what she is talking about, with respect to Fano planes, see the diagrams at this post:
http://carlbrannen.wordpress.com/2007/10/04/fict
Uh, in the comments, "Kea" is Marni Sheppeard, and "Kneemo" is Michael Rios. The drawings show how to calculate topological phase for the Pauli MUBs. I don't know if they have much to do with Fano planes but the higher math types seemed interested.
By the way, regarding your essay, an interesting paper has come by on arXiv that sort of agrees with both of our papers. See:
http://arxiv.org/abs/0901.4917
and other papers by Walter Smilga.
The paper gives a derivation of a rather accurate formula for the fine structure constant originally found by Wyler. It's based on the assumption that the correct symmetry group is SO(3,2) rather than Poincare.
This fits in with what I'm doing because I've got two copies of the the time coordinate, that is, the usual time and the absolute age of the universe. So it's quite natural that one would need a larger symmetry group for this. My original work on the fermions was based on extending the Dirac algebra by adding one hidden dimension to it, which amounts to the same thing (since the Dirac algebra is complex, the sign of the additional dimension doesn't effect the algebra any).
And it fits in with what you're doing because this symmetry is related to AdS in some manner. I'm not a gravity guy and can't explain this further.