But I do like the Stephen Wolfram idea of consciousness being the way a computationally bounded observer develops a coherent view of a branching universe.

This is related to compression because it a (lossy!) reduction in information.

I understand that Wolfram is controversial, but the information-transmission-centric view of reality he works with makes a lot of intuitive sense to me.

https://writings.stephenwolfram.com/2021/03/what-is-consciou...

It’s not a well defined ontology yet. So whatever it is, at its irreducible size pinpointing it as a thing in which gives rise to such other things.