The logarithmic stable-pairs rationality and DT/PT correspondence conjecture

Let $(X,D)$ be a logarithmic pair, let $\beta$ be a curve class, let $\mu$ be a relative insertion, and let $\tau_{k_i}(\gamma_i)$ be descendent insertions. Denote the logarithmic stable-pairs partition function by $\mathsf{Z}_{\mathsf{PT}}$ and the normalized logarithmic DT series by $\mathsf{Z}'_{\mathsf{DT}}$. The logarithmic stable-pairs rationality and DT/PT conjecture. For every $\beta$, $\mu$, and insertions $\gamma_1,\ldots,\gamma_r$, the series

$$\mathsf{Z}_{\mathsf{PT}}\left(X,D;q\mid\prod_{i=1}^r\tau_{k_i}(\gamma_i)\mid\mu\right)_\beta$$

is a rational function of $q$. If every $\gamma_i$ has degree at least $2$, then it equals the normalized DT series $\mathsf{Z}'_{\mathsf{DT}}$ from the basic logarithmic Donaldson–Thomas conjecture. This is the expected logarithmic analogue of PT rationality and DT/PT wall crossing; the source gives no proof or resolution.