Chen–Wang conjecture on alpha-invariants and Kähler–Einstein metrics

Let $X$ be a Fano variety with at most quotient singularities, and for each $n\in\mathbb{N}$ let $\mathrm{lct}_{n,2}(X)$ be the infimum of the log canonical thresholds of pencils in $|-nK_X|$. Chen–Wang conjecture. If

$$\mathrm{lct}_{n,2}(X)>\frac{\mathrm{dim}(X)}{\mathrm{dim}(X)+1}$$

for every $n\in\mathbb{N}$, then $X$ is Kähler–Einstein. This is a proposed analytic criterion for the existence of Kähler–Einstein metrics on Fano orbifolds; the supplied text gives no resolution.