Equality of stable and unstable algebra K-theory ranks for mixing Smale spaces

Let $(X,\varphi)$ be a mixing Smale space, and let $S$ and $U$ denote its stable and unstable algebras, respectively. Stable–unstable rank conjecture. One has

$$\operatorname{rank}(K_*(S))=\operatorname{rank}(K_*(U)).$$

This equality predicts that the stable and unstable algebras associated to a mixing Smale space have K-theory groups of the same rank. The source provides no resolution status for this statement.