I am not making claims about other universes. In particular I am not asserting platonic idealism is true. All I am saying is "2+2=4" is an a priori claim and you don't use rules for incorporating evidence for such claims, as you seemed to imply in your original post.

Please explain the miraculous correspondence to apples and earplugs, then.

I confess that I'm also not entirely sure what you mean by "a priori" or why you think it requires no evidence to locate an "a priori claim" like "2 + 2 = 4" in the vast space of possible a priori claims that includes "2 + 2 = 498034". I'm suspicious of claims that supposedly do not require justification and yet seem to be uniquely preferred within a rather large space of possibilities. Are you sure "a priori" isn't just functioning as a semantic stopsign?

I'll accept as divine any entity that can consistently reduce the entropy of a closed, isolated system

This could just be a manifestation of an entity running our world as a computer simulation. Or even simpler, it could be an alien that knows an important fact you don't know about the real laws of physics. Even if the entity is running our world as a computer simulation, it could itself be made of atoms, go to the bathroom, have a boss screaming at it, etc.

As Damien Broderick observed: "If you build a snazzy alife sim ... you'd be a kind of bridging `first cause', and might even have the power to intervene in their lives - even obliterate their entire experienced cosmos - but that wouldn't make you a god in any interesting sense. Gods are ontologically distinct from creatures, or they're not worth the paper they're written on."