I’ve read through your GR part. Just to counter all the negativity here, congrats for pulling this off! I felt your papers do a much better job in explaining what’s actually the idea. Probably would be better to directly link to them here on HN. I’m a bit rusty but everything you write seems very reasonable to me. One thing I was a bit nervous about, and correct me if I’m wrong, is that you seem to somewhat artificially put in “causal invariance” by restricting all hyper graphs you consider to those that have this property. This isn’t obvious from the rule itself and it seems like it could just go wrong at one point deep into the time evolution. Are you worried about that?

Edit: Additionally the model seems very flexible. To the point that I’m unsure whether it’s surprising to be able to recover GR and other properties. I’m out of my depth here but given that string theory seems to face a similar problem of model selection have you looked at equivalences between those or does this not make sense in your eyes?