K-Theoretic Classification of Simple Separable Nuclear C*-Algebras via Transfinite Inductive Limits

Mathematical Applications of Science Fiction We present a rigorous classification theorem for the classof simple, separable, unital, nuclear, Z-stable C*-algebrassatisfying the Universal Coefficient Theorem (UCT). Byextending the Elliott classification program through a trans-finite inductive limit analysis, we establish that two suchalgebras A and B are isomorphic if and only if there existsan isomorphism of their Elliott invariants Ell(A) ∼= Ell(B).We introduce the notion of transfinite approximate unitaryequivalence and prove a generalized existence and uniquenesstheorem in KK-theory. This work unifies the Kirchberg-Phillips classification of purely infinite algebras and theGong-Lin-Niu classification of stably finite algebras under asingle hyper-rigorous framework involving the Cuntz semi-group and the Jiang-Su algebra Z.