Bodirsky–Pinsker tractability conjecture for reducts of finitely bounded homogeneous structures

Let $fmathbb A$ be a finite-signature reduct of a finitely bounded homogeneous structure. Let $fmathbb C$ be an expansion of the model-complete core of $fmathbb A$ by finitely many constants, and let $\operatorname{Pol}(fmathbb C)$ denote its polymorphism clone. Let $fmathscr P$ denote the clone of projections.

Bodirsky–Pinsker tractability conjecture. If the model-complete core of $fmathbb A$ has no such expansion $fmathbb C$ for which $\operatorname{Pol}(fmathbb C)$ has a continuous clone homomorphism to $fmathscr P$, then

$$\operatorname{CSP}(fmathbb A)\text{ is in P}.$$

This is the infinite-domain tractability conjecture for reducts of finitely bounded homogeneous structures, attributed in the source to Bodirsky and Pinsker. The supplied text does not state whether it has been resolved.