Nonnegative Q-curvature and scalar curvature imply nonnegative Ricci curvature

Let $(M^4,g)$ be a complete four-dimensional Riemannian manifold. Nonnegative curvature implication conjecture. If

$$Q_g\geq 0 \quad\text{and}\quad R_g\geq 0,$$

then

$$\operatorname{Ric}_g\geq 0.$$

This is motivated by results for conformally flat four-manifolds and is presently stated as a conjectural extension to complete four-manifolds. The source gives no general proof or resolution.