Thanks for the feedback. I'll reply to your concerns as best I can.

As far as I can tell, this is basically what you're saying, although what you mean by the reasonableness of our axioms is unclear to me.

I didn't require the axioms to be reasonable in this approach, except, of course, to the extent that their reasonableness causes people to generally accept them in common usage.

Although perhaps you're saying that the math structures have no identity in and of themselves, existing solely in this framework of claim verification. But in that case, the resolution is tautological, and I'm not sure it really gets to the heart of that question.

That is indeed what I'm saying, but I disagree that it's tautological. To the extent that my framework handles difficult problems and paradoxes in a satisfactory way, that is its non-tautological substantiation, as it shows how you don't need to appeal to concepts outside of what I have reduced math to.

I disagree about your negative conclusion of math making new predictions a priori. There is the following underlying problem. The conditions of the reality in general do not exactly match the conditions of the math, or at least, this is not verifiable in general. Hence you can never be sure that your isomorphism between math and reality is strictly correct. But that means that a priori mathematical reasoning is the de facto standard (in general). Obviously there are some special cases like adding apples or rocks together which seems to be fully correspondent, but in most cases, the isomorphism may be unverifiable.

I mostly agree, but refer back to the causal diagram. As a standard Bayesian rule, you will never have 100% certainty on any of your premises or conclusions. However, failure of the predicted causal implication to hold ("adding two rocks to two rocks will yield four rocks") needn't have the same impact on your degree of belief in each of its causal parents. You can do a lot more to verify your math than to verify the isomorphism to something physical.

If the isomorphism has a lot of evidence favoring it, then the math can tell you surprising things about particular regions of the domain of supposed applicability, which turn out to be true. This is the essence of science and engineering. My point here is only that the math's applicability to the universe always depends on the empirical validity of the isomorphism, which you might miss if you view the output of math as being the critical step in an insight.

That's why it's amazing that it works.

I think the amazingness will eventually be demystified by a common factor that caused both our use of math and the universe's frequent close isomorphisms thereto.

Regarding the evidence for the truthfulness of math statements... this "truthfulness" just follows by construction from within the original framework. Not sure what you were getting at in that section.

Yes, and the framework can be relevant or irrelevant to physical systems; people are more likely to be referring to axiom sets that are relevant (have an isomorphism) to physical systems.