The toric transversality conjecture for Frobenius structure counts

Let $(Y,D)$ be a Fano pair, let $q_1,\ldots,q_s\in B(\mathbb{Z})$, and let $N_{\beta}(q_1,\ldots,q_s)$ be the logarithmic Gromov–Witten number defined by integrating $\operatorname{ev}_{s+1}^*[\operatorname{pt}]\cdot\widetilde{\psi}_{s+1}^{s-1}$ over the relevant virtual fundamental class.

Toric transversality conjecture. In the definition of $N_{\beta}(q_1,\ldots,q_s)$, all curves in $\mathcal{M}^{\log}_{0,\Delta_{\mathbf q}}(\widetilde{Y}^{\dagger},\beta)$ satisfying generic representatives of the conditions $\operatorname{ev}_{s+1}^*[\operatorname{pt}]$ and $\widetilde{\psi}_{s+1}^{s-1}$ are torically transverse.

This is an additional expected property of the curves contributing to the Gromov–Witten counts in the weak Frobenius structure conjecture. The parser supplies no evidence that it has been resolved.