Perverse stable-pair partition-function conjecture for nodal K3 fibrations

Let $\widetilde{X}$ be the non-projective threefold in the nodal K3 fibration, and let $\mathop{\rm PT}\nolimits(\widetilde{X})$, $\mathop{\rm PT}\nolimits^h(\widetilde{X})$, and $\mathop{\rm PT}\nolimits^{\rm per}(\widetilde{X})$ denote respectively the stable-pair, horizontal stable-pair, and perverse stable-pair partition functions, with

$$\mathop{\rm PT}\nolimits^{\rm per}(\widetilde{X})=\sum_{n,\beta}P_{n,\beta}^{\rm per}q^nt^\beta.$$

Perverse stable-pair partition-function conjecture. The partition functions satisfy

$$\frac{\mathop{\rm PT}\nolimits(\widetilde{X})}{\mathop{\rm PT}\nolimits^h(\widetilde{X})}=\mathop{\rm PT}\nolimits^{\rm per}(\widetilde{X}).$$

This conjectural identity expresses the contribution of perverse stable pairs as the quotient of the full and horizontal stable-pair theories. The source does not provide evidence resolving the conjecture.