Clopen predicate conjecture for d-minimal expansions of the real field

Let $\mathcal R$ be a d-minimal expansion of $\bar{\mathbb{R}}$. Let $X \subseteq \mathbb{R}^n$ be a manifold definable in $\mathcal R$, and let $Y \subseteq X$ be clopen in $X$. Clopen predicate conjecture. The expansion $\langle \bar{\mathbb{R}},Y\rangle$, obtained by adding a predicate for $Y$ to $\bar{\mathbb{R}}$, is also d-minimal. This concerns preservation of d-minimality under naming a clopen definable subset of a definable manifold; the supplied text does not state whether the conjecture has been resolved.