Conjecture on Fano complex contact manifolds with second Betti number one

Let $Y$ be a Fano complex contact manifold with second Betti number $b_2=1$. For a simple Lie group $G$, let $\mathfrak{g}$ denote its Lie algebra, and let $G$ act on the projective space $\mathbb{P}(\mathfrak{g})$ by the adjoint action. Fano contact manifold conjecture. $Y$ is a homogeneous variety that is the unique closed orbit of the adjoint action of some simple Lie group $G$ on $\mathbb{P}(\mathfrak{g})$. This is a classification conjecture for the remaining case in the structure theory of complex contact manifolds after the numerically effective canonical-divisor case has been excluded. The source does not provide evidence of resolution.