Weak Elliott conjecture via the total Cuntz semigroup

Let $A$ be a unital, separable, nuclear ${\rm C}^*$-algebra of real rank zero and stable rank one, and let $\underline{\mathrm{Cu}}_u(A)$ denote its total Cuntz semigroup invariant. Weak Elliott conjecture. The invariant $\underline{\mathrm{Cu}}_u(A)$ is complete for such ${\rm C}^*$-algebras. The total Cuntz semigroup distinguishes the paper's counterexample and yields classification results for a broad class of extensions, but the proposed classification for all unital algebras in this class remains open.