Higher-genus Ooguri–Vafa integrality conjecture for chromatic Lagrangian wavefunctions

Let $L$ be a Lagrangian with boundary $S_\Gamma$, let $A$ be a choice of phase and framing, and let $\Psi_\Gamma^{(A)}$ be the corresponding algebraic wavefunction. For coordinates $(x_1,\ldots,x_g)$, write $x^d=x_1^{d_1}\cdots x_g^{d_g}$. Higher-genus Ooguri–Vafa integrality conjecture. The wavefunction $\Psi_\Gamma^{(A)}$ is the generating function for all-genus open Gromov–Witten invariants of $L$ in framing $A$, with expansion

$$\Psi_\Gamma^{(A)}(x_1,\ldots,x_g)=\prod_{s\geq 0}\prod_{d\in\mathbb{Z}_{\geq 0}^g\setminus\{0\}}\Phi(x^dq^s)^{n_{d,s}^{(A)}},$$

where

$$\Phi(x)=\prod_{n\geq 0}\frac{1}{1-q^n x}$$

and $n_{d,s}^{(A)}$ are integers. This is the proposed all-genus quantization of the disk-level Ooguri–Vafa expansion; the relevant open Gromov–Witten theory is not yet rigorously defined in the generality considered.