Strong Elliott conjecture for K-pure real-rank-zero C*-algebras

Let $A$ be a separable, nuclear, K-pure ${\rm C}^*$-algebra of real rank zero and stable rank one. Let $({\rm\underline{K}}(A),{\rm\underline{K}}(A)_+,\Sigma A)_{\rm \Lambda}$ consist of total K-theory, its positive cone, and the scale, with the indicated coefficient structure. Strong Elliott conjecture. The invariant

$$({\rm\underline{K}}(A),{\rm\underline{K}}(A)_+,\Sigma A)_{\rm \Lambda}$$

is complete for such ${\rm C}^*$-algebras. This is presented as a proposed refinement after the unrestricted real-rank-zero classification claim is disproved; the paper proves classification results for K-pure extensions but does not establish this full formulation.