Phil,
From your essay, "There is no general consensus yet on how to replace space and time but there is a widespread view that the space-time manifold as we knew it in general relativity is no longer the accepted starting point. It is just an approximation to some other unknown mathematical structure."
Space-time has become a distorted abstraction precisely because it did not have a proper mathematical structure. We have possessed the necessary knowledge, mathematical for 2,000 years, and physical law for 200 years, to establish the mathematical structure for space (distance) and time (event duration).
Some sixty years ago, the final piece of knowledge came into our possession that allowed the integration of space-time into a well established mathematical structure. The mathematical process, which I refer to as the "Methodology", was published in the July/August 2011 IEEE Potentials, titled, "A methodology to define physical constants using mathematical constants".
IEEE Methodology
Since Jan 2011, IEEE does not allow authors to post their IEEE published papers on their academic or personal websites. A post-print is available at:
Post-print Methodology
The concept in the Methodology is not taught in text books.