Convexity conjecture for strongly Ricci-negative derivations

Let $\mathfrak{n}$ be a nilpotent Lie algebra, let $\mathfrak{t}(\mathfrak{n})$ be a maximal torus of diagonalizable derivations, and let $\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}$ denote the corresponding strongly Ricci-negative cone. Strong Ricci-negativity cone conjecture. The cone $\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}$ is open in $\mathfrak{t}(\mathfrak{n})$ and convex. This is known for Heisenberg and filiform Lie algebras and for every nilpotent Lie algebra of dimension at most five, but remains open in general.