Conifold Gap Conjecture for local $\mathbb{P}^2$

Let $g\text{?}$ Let $t_{\rm CF}$ be the local conifold coordinate and define the genus-$g$ conifold Gromov–Witten potential of $K_{\mathbb{P}^2}$ by

$$\mathrm{GW}_g^{\rm CF} \coloneqq \mathrm{GW}_g^{\rm LR}\big|_{\mathsf{q}_{\rm LR} \to \mathsf{q}_{\rm CF}}.$$

Here $B_n$ denotes the $n^{\rm th}$ Bernoulli number, defined by

$$\frac{t}{\mathrm{e}^{t}-1} \coloneqq \sum_{n \geq 0} \frac{B_n t^n}{n!}.$$

Conifold Gap property for $K_{\mathbb{P}^2}$. For $g \in \mathbb{Z}_{\geq 2}$, near $t_{\rm CF}=0$,

$$\mathrm{GW}_g^{\rm CF} = \frac{3^{g-1} B_{2g}}{2g(2g-2)} t_{\rm CF}^{2-2g} + \mathcal{O}(1).$$

This conjectural property predicts the complete polar part of the Laurent expansion at the conifold point and removes the remaining $2g-1$-dimensional ambiguity in the higher-genus potential up to the additive constant map term. The supplied text does not establish whether the conjecture has been resolved.