Hi Michael,
Thank you for your kind words. I think we are on the same page as far as the understanding my central message is concerned, but we may have different views about some of the details.
In particular, you are correct to read my disproof as a proof that QT is not fundamental. The credit for this observation, however, must go first to Einstein, and then to Bell, before my work is even considered. Einstein argued most of his life that QT is not a fundamental theory, and Bell's work (which is based on the earlier work on hidden variables by von Neumann) clarified and quantified Einstein's position tremendously. My work is entirely in the tradition of Einstein, von Neumann, and Bell, but of course these giants do not consider going beyond the algebra of the real line, whereas both you and I consider the most general division algebra possible, namely the octonionic algebra, associated with S7. I too feel that our work is related, but I must admit that I haven't had time to digest some of your arguments (these days I am preoccupied in clarifying the relationship between SU(2) and SO(3) even further to understand the issue of "flatness" you alluded to above).
You have rightly raised the question about my usage of the word "local." I have used a very precise definition of "local" provided by Bell. This definition is theory-independent. In particular, it is independent of relativistic considerations. On the other hand, it may not remain valid if the space-time metric itself changes its signature during the course of dynamics, say, of an EPR pair. I am not sure whether a relativistic change in metric signature of the kind you have considered is captured in the global structure of the S3 function space. My feeling is that if such a change in signature is allowed then strong quantum correlations would be wiped out. That is not such a bad thing, however, for we do observe both quantum as well as classical correlations. In fact, more often than not we observe classical correlations rather than quantum correlations.
I think you are right to think that the same argument would apply to the gauge orientation x of the internal particle property space of gauge symmetries, with S7 substituted for S3. But the details here are beyond my field of expertise, so I am unable to be all that confident about this.
The octonionic S7 is indeed flat, and it is this discipline of "flatness" of S7 that is responsible for the strong quantum correlations. That is my claim in any case.
Thanks again for your kind words about my book. It is good to be appreciated.
Best,
Joy