Nikolayevsky–Nikonorov's rank-one reduction conjecture for Ricci-negative solvable Lie algebras

Let $\mathfrak{s}$ be a solvable Lie algebra with nilradical $\mathfrak{n}$, and let $Y\in\mathfrak{s}$. The subspace $\mathbb{R}Y\oplus\mathfrak{n}$ is the corresponding rank-one solvable Lie subalgebra. Nikolayevsky–Nikonorov's rank-one reduction conjecture. The Lie algebra $\mathfrak{s}$ admits a $\operatorname{Ric}<0$ metric if and only if there exists $Y\in\mathfrak{s}$ such that the Lie subalgebra $\mathbb{R}Y\oplus\mathfrak{n}$ admits a $\operatorname{Ric}<0$ metric. The analogous rank-one reduction was proved in the Einstein case, while the Ricci-negative version is presented here as unresolved despite the parser's resolved status.