Zinger's comparison conjecture for Fano threefold Gromov–Witten invariants

Let $X$ be a Fano threefold, let $\beta$ be a curve class, and let $N_\beta^g(\gamma)$ and $r_\beta^h(\gamma)$ denote the standard and reduced Gromov–Witten invariants with insertions $\gamma$. Define $C_{h,\beta}^X(g)$ by

$$\sum_{g\geq 0}C_{h,\beta}^X(g)t^{2g}=\left(\frac{\sin (t/2)}{t/2}\right)^{2h-2-K_X\cdot\beta}.$$

Zinger's comparison conjecture. One has

$$N_\beta^g(\gamma)=\sum_{h=0}^g C^X_{h,\beta}(g-h)r_\beta^h(\gamma).$$

This gives the conjectural relation between standard and reduced invariants for Fano threefolds, where reduced invariants are expected to agree with Gopakumar–Vafa invariants. The surrounding text does not report a proof of this full statement.