Katz product expansion conjecture for the PT generating series

Let $X$ be a Calabi–Yau $3$-fold, let $\beta>0$ range over effective curve classes, and let $\mathop{\rm PT}\nolimits(X)$ be the Pandharipande–Thomas generating series. Katz product expansion conjecture. There are integers $n_g^\beta\in\mathbb Z$ for $g\geq 0$ and $\beta\in H_2(X,\mathbb Z)$ such that

$$\mathop{\rm PT}\nolimits(X)=\prod_{\beta>0}\left(\prod_{j=1}^{\infty}(1-(-q)^jt^\beta)^{j n_0^\beta}\cdot\prod_{g=1}^{\infty}\prod_{k=0}^{2g-2}(1-(-q)^{g-1-k}t^\beta)^{(-1)^{k+g}n_g^\beta\binom{2g-2}{k}}\right).$$

The formula is a conjectural product expression for the PT series in terms of Gopakumar–Vafa invariants and leads to predicted multicover formulas for curve-counting invariants.