The pluricomplex Green function minimizer conjecture

Let $X$ be a Fano manifold and let $L=-K_X$. Assume that $\delta<1$, and let $G$ be a pluricomplex Green function obtained as an $L^1$ limit of normalized potentials along Aubin's continuity path. Pluricomplex Green function minimizer conjecture. The function $G$ is a minimizer of $\delta_{\mathrm{pp}}$. This is a focused restatement of the minimizer claim in the Fano case; the source gives no evidence that it has been resolved.