I think the problem of enumerating these possibilities is impossible. You should notice that even the conventional possibility, quantum field theory somehow modified to have gravity and cosmology, is incomplete. It describes a mathematical construct, but it doesn’t describe how our experiences fit into that construct. It’s possible that just by looking at this mathematical object in a different way, you can find a different universe. That’s why this point-of-view information is actually important. Looking just at the possibilities where the universe is computable, enumerating Turing machines looks sufficient, but it is not. Turing machines don’t describe where we should look for ourselves in them, which is the most important part of the business. If we allow this, we should also allow the universe to be described by finite binary strings, which at times code for a Turing machine where we can be found in a certain point of view, but at other times code for various more powerful modes of computation. We can even say there is only one possibility, the totality of mathematical objects being the universe, which we can find ourselves in in very many different ways (this is the Tegmark level 4 multiverse theory).
So we can’t truly enumerate all the possibilities, even assuming a casual universe, since a casual diagram isn’t really capable of fully describing a possibility. It might be reasonable at certain times to enumerate these things anyways, and deal with this degeneracy in a ad hoc way. In that case, there would be nothing wrong with also making an ad hoc assumption along the lines of saying that the universe must be Turing computable (in which case you can simply list Turing machines).
I think the problem of enumerating these possibilities is impossible. You should notice that even the conventional possibility, quantum field theory somehow modified to have gravity and cosmology, is incomplete. It describes a mathematical construct, but it doesn’t describe how our experiences fit into that construct. It’s possible that just by looking at this mathematical object in a different way, you can find a different universe. That’s why this point-of-view information is actually important. Looking just at the possibilities where the universe is computable, enumerating Turing machines looks sufficient, but it is not. Turing machines don’t describe where we should look for ourselves in them, which is the most important part of the business. If we allow this, we should also allow the universe to be described by finite binary strings, which at times code for a Turing machine where we can be found in a certain point of view, but at other times code for various more powerful modes of computation. We can even say there is only one possibility, the totality of mathematical objects being the universe, which we can find ourselves in in very many different ways (this is the Tegmark level 4 multiverse theory).
So we can’t truly enumerate all the possibilities, even assuming a casual universe, since a casual diagram isn’t really capable of fully describing a possibility. It might be reasonable at certain times to enumerate these things anyways, and deal with this degeneracy in a ad hoc way. In that case, there would be nothing wrong with also making an ad hoc assumption along the lines of saying that the universe must be Turing computable (in which case you can simply list Turing machines).