Except cryptography usually rely on mathematical proofs. I'm not aware of such possibility for distributed systems. I know Lamport did work on that subject, but i'm not sure if you can equate a TLA+ proof on some properties to a mathematical proof about the structure of numbers, nor do i know if ethereum even has a TLA+ proof or equivalent of anything regarding the PoS protocol (i honestly don't know, so i may be completely wrong).
But the main issue in provable security is that you're trying to prove real world things with math, and so far we're quite bad at it. The more mathematical the thing you want to prove is, the better.
