RCD versus smooth positive Ricci curvature conjecture

There exist an integer $n\ge 4$ and a smooth simply connected $n$-manifold $M^n$ such that there is no smooth metric $g$ on $M^n$ with $\operatorname{Ric}\ge n-1$, while there is a distance $\mathsf{d}$ compatible with the topology of $M^n$ for which $(M^n,\mathsf{d},\mathscr{H}^n)$ is an $\operatorname{RCD}(n-1,n)$ space.

RCD versus smooth curvature conjecture. Such an $n$ and $M^n$ exist.

The conjecture asks whether synthetic Ricci curvature can occur on a simply connected smooth manifold where the corresponding smooth Ricci lower bound is impossible. The source presents it as an open question at the end of the survey and gives no known resolution.