2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64334We prove that a simple, separable, nuclear, purely infinite classifiable $C^*$-algebra is weakly semiprojective if and only if its $K$-groups are direct sums of cyclic groups.10 pages, 3 figures. Drastically revised: a major technical argument has been removed to a separate articleOperator AlgebrasPrimary 46L05, 46L80. Secondary 22A22text