Rationality conjecture for admissible W-algebras

Let $\mathfrak{g}$ be a simple Lie algebra, $f$ a nilpotent element, and $k$ an admissible level. Let $\mathbb{O}_k$ denote the corresponding nilpotent orbit. Rationality conjecture. If $f\in\mathbb{O}_k$, then the simple $W$-algebra $\mathscr{W}_k(\mathfrak{g},f)$ is rational. The source records proofs in several cases, including principal $f$, type $A$, and further cases, but not in full generality.