Given that Wolfram Physics Project is background independent I am curious how it interacts with formalism and predictions of "Shape Dynamics" - a theory of gravity locally similar to General Relativity but with different global implications.
I will not go into all the detail what makes SD stand out from GR (https://arxiv.org/abs/1409.0105 has an SD tutorial which is a fascinating, but very technical in places, read). Similarities with the Wolfram Physics Project is that both are background independent and have an arrow of time. SD also has a relativity of size (implying that the length of an object is only measured locally by using other objects as a reference, objects far away from each other cannot be properly compared). Of course, in the Wolfram project, distance between elements is also somewhat arbitrary (if I understand it correctly).
However, SD seems to really shine when it comes to solving for singularities (whether black holes or the big bang). My limited understanding of those solutions is that black holes can form pocket universes and that the big bang can be traced back to a big crunch of an earlier universe.
My last paragraph is the most speculative, so please keep it in mind. If the universe is a branch tree of black holes within black holes with initial conditions being slightly different for each new daughter universe (as Lee Smolin proposed in his 1997 book "The Life of the Cosmos") then it has a direct bearing on this project. Another words, instead of randomly looking for a set of initial conditions plus a rule to start our computational universe, we can try to guess what the overall rule is. For example, Lee Smolin proposed that it could be some rule that maximizes the number of black holes in a universe.