Relative descendent GW/Pairs correspondence

Let $X$ be a nonsingular $3$-fold with a nonsingular divisor $D\subset X$, let $0\ne\beta\in H_2(X,\mathbb Z)$), and let $\mu$ be a cohomology-weighted partition of $\int_\beta[D]$. For $\gamma_i\in H^*(X,\mathbb Q)$), let $\overline{\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_\ell-1}(\gamma_\ell)}$ be the relative descendent correspondence formed using the relative diagonal and the logarithmic tangent bundle $T_X[-D]$.

Relative descendent GW/Pairs correspondence. Under the variable change $-q=e^{iu}$,

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

The conjecture also includes rationality in $q$ of the stable-pairs descendent series, which makes the change of variables well-defined. No resolution status is supplied.