It's just not what the word axiom means nor how anyone uses it. An axiom is unprovable by definition - is it a thing we accept to be true because it is useful to do so (e.g. there exists an empty set)

"Provably Correct Axiom" is nonsense. An axiom is unprovable.

Just "provably correct" would've been fine. This chess stuff is hilariously pretentious.