Stable-pairs descendent correspondence for relative 3-folds

Let $X/D$ be a relative $3$-fold, let $\beta$ be a curve class, let $\mu$ be a relative boundary condition, and let $\gamma_i\in H^*(X)$. The barred relative descendent insertion is defined using the correspondence matrix with the substitution $c_i=c_i(T_X[-D])$. Relative stable-pairs descendent correspondence conjecture. Under the variable change $-q=e^{iu}$,

$$(-q)^{-d_\beta/2}\mathsf Z_{\mathsf P}\Big(X/D;q\ \Big|\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_\ell-1}(\gamma_\ell)\ \Big|\ \mu\Big)_\beta=(-iu)^{d_\beta+\ell(\mu)-|\mu|}\mathsf Z'_{\mathsf{GW}}\Big(X/D;u\ \Big|\overline{\tau_{a_1-1}(\gamma_1)\cdots\tau_{\alpha_\ell-1}(\gamma_\ell)}\ \Big|\ \mu\Big)_\beta.$$

The statement extends the absolute descendent correspondence to relative geometries; the supplied text does not report a general proof.