The Bertola–Yang weak open $r$-spin comparison conjecture

Fix $r\geq 2$, let $\overline g$ denote the doubled genus, and suppose $b,m>0$. Let the superscript $r\mathrm{BY}$ denote the Bertola–Yang intersection numbers and $r\star$ the numbers defined by the proposed partition function. Bertola–Yang comparison conjecture. One has

$$\left\langle\tau_{d_1}^{\circ}(a_1)\cdots\tau_{d_n}^{\circ}(a_n)\tau_{k_1}^{\partial}\cdots\tau_{k_m}^{\partial}\right\rangle^{r\mathrm{BY}}_{\overline g;n;m}=\sum_{\substack{g,b\in\mathbb N\g+b/2=\overline g}}\left\langle\tau_{d_1}^{\circ}(a_1)\cdots\tau_{d_n}^{\circ}(a_n)\tau_{k_1}^{\partial}\cdots\tau_{k_m}^{\partial}\right\rangle^{r\star}_{g,n;b,m}.$$

This is explicitly presented as a weaker prediction, restricted to $b,m>0$, relating the Bertola–Yang quantities to the proposed open $r$-spin theory; the source provides no resolution.