Here's my guess as to how the universality hypothesis a.k.a. natural abstractions will turn out. (This is not written to be particularly understandable.)
Totally baseless conjecture that I have not thought about for very long; chaos is identical to Turing completeness. All dynamical systems that demonstrate chaotic behavior are Turing complete (or at least implement an undecidable procedure).
Has anyone heard of an established connection here?
Might look at Wolfram's work. One of the major themes of his CA classification project is that chaotic (in some sense, possibly not the rigorous ergodic dynamics definition) rulesets are not Turing-complete; only CAs which are in an intermediate region of complexity/simplicity have ever been shown to be TC.
Maybe you already thought of this, but it might be a nice project for someone to take the unfinished drafts you've published, talk to you, and then clean them up for you. Apprentice/student kind of thing. (I'm not personally interested in this, though.)
I like that idea! I definitely welcome people to do that as practice in distillation/research, and to make their own polished posts of the content. (Although I'm not sure how interested I would be in having said person be mostly helping me get the posts "over the finish line".)