Every self-contained mathematical structure is also contained within larger mathematical structures. For example, our universe must exist both as a stand-alone mathematical structure, and also as simulations within larger universes, and we have preferences both for the smaller mathematical structure, as well as the larger ones. I'm not sure if you've already taken that into account, but thought I'd point it out in case you haven't.

It's useless to discuss fine points in an informal description like this. At least, what is meant by "mathematical structures" should be understood, depending on that your point may be correct, wrong, or meaningless. In this case, I simply referred to taking the problem inside a limited universe of discourse, as opposed to freely interacting with the world.