Stable-pairs descendent correspondence for absolute 3-folds

Let $X$ be a nonsingular projective $3$-fold, let $\beta\in H_2(X,\mathbb Z)$, let $d_\beta=\int_\beta c_1(X)$, and let $\gamma_i\in H^*(X)$. The barred descendent insertion $\overline{\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_\ell-1}(\gamma_\ell)}$ is defined using the correspondence matrix described in the source. Stable-pairs descendent correspondence conjecture. Under the variable change $-q=e^{iu}$,

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

This is the stable-pairs/Gromov–Witten descendent correspondence proposed in the cited work; the supplied text gives no resolution of the general statement.