My former student Newshaw Bahreyni and I have published our paper on a potential foundation for emergent space-time at the Journal of Mathematical Physics. Here is the abstract:

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.

We will be presenting this work, in addition to other more recent findings at the upcoming workshop titled BeyondSpaceTime in San Diego in March.