BPS Lie algebra identification conjecture for quivers

Let $Q$ be a quiver, let $\bar{\mathfrak{n}}_Q$ be the graded BPS Lie algebra arising from the filtration on $H_*(T^*\mathcal{M}_Q)$, and let $\widetilde{\mathfrak{n}}_Q$ be the positive subalgebra of the graded Borcherds algebra $\widetilde{\mathfrak{g}}_Q$. BPS Lie algebra identification conjecture. The graded Lie algebra $\bar{\mathfrak{n}}_Q$ is isomorphic to the positive subalgebra $\widetilde{\mathfrak{n}}_Q$ of $\widetilde{\mathfrak{g}}_Q$.

This conjecture would identify the geometric BPS Lie algebra with the positive part of the putative graded Borcherds algebra; the supplied text does not state a resolution.