Gromov's rational inessentiality conjecture

Let $M$ be a closed orientable $n$-manifold with universal cover $\widetilde M$. Suppose that

$$\dim_{mc}\widetilde M<n.$$

Gromov's rational inessentiality conjecture. Then $M$ is not rationally essential.

The conjecture relates a strict macroscopic-dimension bound to rational essentialness. The supplied text attributes it to Gromov and gives no evidence that it has been resolved.