The solvable-radical sequence conjecture for finite-dimensional Lie algebras

Let $L$ be a finite-dimensional Lie algebra. For a sequence $\overrightarrow{u}=\overrightarrow{u}(x,y)$, write $L(\overrightarrow{u})$ for the corresponding ideal and let the solvable radical of $L$ be its largest solvable ideal. Solvable-radical sequence conjecture. There is a sequence $\overrightarrow{u}=\overrightarrow{u}(x,y)$ such that, for every finite-dimensional Lie algebra $L$, the solvable radical of $L$ coincides with $L(\overrightarrow{u})$. The conjecture proposes a uniform Engel-like description of solvable radicals for finite-dimensional Lie algebras; the supplied text gives no resolution status.