Stable-pair/Donaldson–Thomas partition-function correspondence for logarithmic Calabi–Yau 3-folds

Let $\bold X$ be a logarithmic Calabi–Yau 3-fold and let $Z_{DT}(\bold X)_\beta$ and $Z_{PT}(\bold X)_\beta$ be the Donaldson–Thomas and stable-pair partition functions in the lagrangian-cycle space associated with $D^{[\beta]}$. Define

$$Z'_{DT}(\bold X)_\beta=\frac{Z_{DT}(\bold X)_\beta}{Z_{DT}(\bold X)_0}.$$

Stable-pair/Donaldson–Thomas correspondence conjecture.

$$Z'_{DT}(\bold X)_\beta=Z_{PT}(\bold X)_\beta$$

within

$$\operatorname{Lag}(D^{[\beta]})^-\otimes \mathbb Z[[q^{\frac 12},q^{-\frac 12}]].$$

This is a logarithmic refinement of the stable-pair/Donaldson–Thomas correspondence, with the degree-zero Donaldson–Thomas contribution removed. The source gives no resolution, so it remains open.