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.
Sorry but the entire line of argumentation and all it’s chess flavor is miles off the mark. This is not the sound of arguing with someone who studied what they talked about.