The proofs are only correct in as far as you believe in the Axioms of mathematics that those proofs are built on. Stop "believing in" the axioms and the proofs are no longer true or even meaningful.

But it is still the case that IF the axioms hold, THEN the proofs are either valid or not.

So it's conditional reality. Now make that fit within your usual realistic philosophy...

Easy. There exist contingency relationships between axioms and theorems provable from those axioms.

Oh, yeas, your proof is quite real. And it's completely meaningless, being all about imaginary things.

It can only have any meaning if you adhere to some scientific model.

At this point you've deviated so much from the OP discussion that you could as well talk about angels dancing in pinheads. Any quantification of them is as real as your proof.