Pandharipande–Thomas correspondence between reduced DT and PT series

Let $X$ be a Calabi–Yau $3$-fold, let $\beta>0$ be an effective curve class, and let $\mathop{\rm DT}\nolimits'_{\beta}(X)$ and $\mathop{\rm PT}\nolimits_{\beta}(X)$ denote the degree-$\beta$ coefficients of the reduced Donaldson–Thomas and Pandharipande–Thomas generating series, respectively. Pandharipande–Thomas correspondence.

$$\mathop{\rm DT}\nolimits'_{\beta}(X)=\mathop{\rm PT}\nolimits_{\beta}(X).$$

This conjecture identifies two curve-counting theories built from different moduli problems and is a central part of the DT/PT correspondence.