The Univalent Correspondence: How Six Perspectives on Number Become One

This synthesis paper unifies the six-part series. Under Voevodsky's univalence axiom, the four perspectives of Papers III through VI are not analogous but literally identical: an initial successor structure, a representing presheaf, a contractible Σ-type of NNO structures, and a structural invariant of arithmetic models are four faces of one ∞-groupoid. We name this identification the univalent correspondence, building on the four-way computational tetrad of Curry, Howard, Lambek, and Voevodsky.