Connell–Ruan–Wang's equivalence conjecture for nonpositively curved four-manifolds

Let $M$ be a closed nonpositively curved $4$-manifold, and let $\|M\|$ denote its simplicial volume and $\chi(M)$ its Euler characteristic. Connell–Ruan–Wang's equivalence conjecture. Then

$$\|M\| = 0 \quad\Longleftrightarrow\quad \chi(M) = 0.$$

This conjecture would characterize vanishing simplicial volume for closed nonpositively curved four-manifolds by vanishing Euler characteristic. The source states that it was proposed by Connell, Ruan, and Wang and that it would imply the relevant positivity conjecture in dimension four; the conjecture remains open.