We can apply all this to spin foams / spin nets!

The key question is this. Is there a phase which leads to smooth space times?

Some promising results! Dittrich & collaborators have found fix points from which one could extract different systems of embedding maps. Those would correspond to different (non-) realisations of ’emergence of space-time).

Task for the future: Expand the theory around this vacuum!

Coming back to the initial question: What is (quantum) space-time? Dittrich suggests the time scales for constructing an answer are ~2500ys. Challenge accepted!