Relative stable pairs/Gromov–Witten descendent correspondence

Let $X$ be a nonsingular projective $3$-fold, let $D\subset X$ be a nonsingular divisor, and let $\gamma_1,\ldots,\gamma_\ell\in H^*(X,\mathbb{Q})$ restrict to zero on $D$. Let $\mu$ be a relative partition, and let $\overline{\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_\ell-1}(\gamma_\ell)}$ be the transformed descendent insertion defined from the correspondence matrix for the logarithmic tangent bundle $T_X[-D]$. Set $-q=e^{iu}$.

Relative descendent GW/Pairs correspondence.

$$(-q)^{-d_\beta/2}\mathsf Z_{\mathsf P}\Big(X/D;q\ \Big|\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_\ell-1}(\gamma_\ell)\ \Big|\mu\Big)_\beta = (-iu)^{d_\beta+\ell(\mu)-|\mu|}\mathsf Z'_{\mathsf{GW}}\Big(X/D;u\ \Big|\overline{\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_\ell-1}(\gamma_\ell)}\ \Big|\mu\Big)_\beta.$$

The conjecture is restricted to insertions vanishing on the relative divisor because the transformed descendent correspondence is subtle for arbitrary classes. The source states that the stable-pairs descendent series is also conjectured to be rational in $q$.