GW descendent series polynomiality in the asymptotic function F3

Let $X$ be a nonsingular projective 3-fold, let $\gamma_i\in H^*(X,\mathbb{C})$, and define

$$F_3(u)=-\sum_{n=0}^{\infty}\frac{B_{2n+2}B_{2n}}{(2n)!(2n+2)}(iu)^{2n-1}.$$

Let $\mathcal{R}$ be the ring of rational functions of $q=-e^{iu}$.

GW descendent polynomiality conjecture. The series

$$\big\langle \tau_{k_1}(\gamma_1)\dots \tau_{k_m}(\gamma_m)\big\rangle_{\beta}^{\mathsf{GW}}$$

is a polynomial in $(\frac{d}{du})^iF_3(u)$ for $0\leq i\leq m$, with coefficients in $\mathcal{R}[u^{\pm1}]$.

This is presented as the Gromov–Witten analogue of the DT descendent polynomiality conjecture and is intended to describe the analytic complexity of the complete non-equivariant GW descendent theory.