Gödel's Incompleteness Theorem applies to arbitrary programs. The AI only has to prove results about specific programs, and it can follow whatever restrictions it needs to make such proofs possible.
The physical world means bit flips are inevitable, but error correcting codes exist. You can apply as much error correction as you like and reduce the probability of failure to an arbitrarily low value.
The physical world means bit flips are inevitable, but error correcting codes exist. You can apply as much error correction as you like and reduce the probability of failure to an arbitrarily low value.