The Short Version
Multiple rigorously established formal connections between classical and quantum physics — including the Correspondence Principle, Ehrenfest's theorem, and the Poisson bracket-to-commutator mapping — are well-documented across peer-reviewed literature and foundational physics textbooks. The claim that "a proven connection exists" is clearly supported. While the full problem of how classical macroscopic behavior completely emerges from quantum mechanics remains an open question, this does not negate the existence of proven connections — it only limits their scope.