Schoen–Yau positive mass conjecture for arbitrary asymptotically flat ends

Let $(M,g)$ be a complete Riemannian manifold of dimension $n obreak\text{{\geq}}3$ which has non-negative scalar curvature. Let $\mathcal{E}\subseteq M$ be a single asymptotically flat end in $M$.

Schoen–Yau's conjecture. The ADM mass of $\mathcal{E}$ is non-negative.

This conjecture extends the positive mass theorem to a single arbitrary asymptotically flat end. In the spin setting it was proved by Bartnik and Chruściel using Witten's method; the supplied source does not indicate a resolution in the general setting.