Stationary GW/PT descendent correspondence beyond toric threefolds

Let $X$ be a nonsingular projective 3-fold, let $\gamma_i\in H^{\geq 2}(X,\mathbb{C})$, and let $\vec{k}=(k_1,\ldots,k_l)$ be a vector of non-negative integers. Define the modified Gromov–Witten insertions $\overline{\mathrm{H}_{k_1}(\gamma_1)\dots\mathrm{H}_{k_l}(\gamma_l)}$, and let $d=\int_\beta c_1$. After the change of variables $-q=e^{iu}$,

Stationary GW/PT correspondence conjecture.

$$\Big\langle\overline{ \mathrm{H}_{k_1}(\gamma_1)\dots \mathrm{H}_{k_l}(\gamma_l)} \Big\rangle_{\beta}^{\mathsf{GW}}=q^{-d/2}\Big\langle \mathrm{H}^{\mathsf{PT}}_{k_1}(\gamma_1)\dots \mathrm{H}^{\mathsf{PT}}_{k_l}(\gamma_l) \Big\rangle_{\beta}^{\mathsf{PT}}.$$

The theorem preceding the conjecture proves this correspondence for nonsingular projective toric 3-folds and classes of degree at least $2$. The conjecture asserts that the toric restriction is unnecessary, while retaining the stationary insertion hypothesis.