Hong and Won's conjecture on the alpha-invariant of a del Pezzo surface

Let $S$ be a smooth del Pezzo surface and let $A$ be an ample divisor on $S$ of one of the specified $\mathbb{P}^2$-, $\mathbb{F}_1$-, or $\mathbb{P}^1\times\mathbb{P}^1$-types. Let $\alpha(S)$ denote the classical alpha-invariant, let $\alpha(S,A)$ denote the alpha-invariant associated with $A$, and let $\alpha_c(S,A)$ be the explicitly defined piecewise quantity for the type of $A$. Hong and Won's conjecture. If

$$\alpha(S)=1,$$

then

$$\alpha(S,A)=\alpha_c(S,A).$$

The conjecture predicts that, when the classical alpha-invariant equals $1$, the alpha-invariant associated with the ample divisor $A$ is given by the stated combinatorial formula. The supplied text does not indicate whether the conjecture has been resolved.