Genus and auxiliary-term formula conjecture for ADE orbifolds

Let $\mathbb{P}^1$ be an orbifold of ADE type, with orbifold-point multiplicities $p$, $q$, and $r$, and let $t_n$ denote the distinguished coordinate appearing in the genus-zero Frobenius structure. Let $G(t)$ be the genus-one $G$-function and let $O_1$ and $O_2$ be the auxiliary quantities defined in the paper. ADE orbifold formula conjecture. For $\mathbb{P}^1$-orbifolds of ADE type,

$$G(t)=-\frac{\log t_n}{24r},\qquad O_1-O_2=\frac16(p^3+q^3+r^3-p-q-r).$$

The formula is proposed after lemmas establishing the corresponding expressions in the $\tilde A$, $\tilde D$, and $\tilde E$ cases. The supplied text does not state whether this conjecture has since been proved or refuted.