  In 2006, Restorff completed the classification of all Cuntz-Krieger algebras
with finitely many ideals (i.e., those that are purely infinite) up to stable
isomorphism. He left open the questions concerning strong classification up to
stable isomorphism and unital classification. In this paper, we address both
questions. We show that any isomorphism between the reduced filtered K-theory
of two Cuntz-Krieger algebras with finitely many ideals lifts to a
*-isomorphism between the stabilized Cuntz-Krieger algebras. As a result, we
also obtain strong unital classification.
