Categorical DT MNOP/PT comparison conjecture

Let $I_n(X,\beta)$ and $P_n(X,\beta)$ be the MNOP and stable-pair moduli spaces, respectively, and let $\mathcal{DT}^{\mathbb{C}^{\ast}}(-)$ denote their $\mathbb{C}^{\ast}$-equivariant categorical DT theories. Categorical DT MNOP/PT comparison conjecture. There exists a fully faithful functor

$$\mathcal{DT}^{\mathbb{C}^{\ast}}(P_n(X,\beta))\hookrightarrow\mathcal{DT}^{\mathbb{C}^{\ast}}(I_n(X,\beta)).$$

This is the categorical analogue of the d-critical flip relating the MNOP and stable-pair moduli spaces; the source does not give a resolution.