Ooguri–Vafa integrality conjecture for the chromatic Lagrangian superpotential

Let $L$ be a Lagrangian with boundary $S_\Gamma$, let $A$ be a choice of phase and framing, and let $W_\Gamma^{(A)}$ be a primitive function whose graph of the differential gives the lifted moduli space of the Lagrangian. For coordinates $(x_1,\ldots,x_g)$ determined by a basis of $H_1(L)$, write $x^d=x_1^{d_1}\cdots x_g^{d_g}$. Ooguri–Vafa integrality conjecture. The superpotential $W_\Gamma^{(A)}$ is the generating function for holomorphic disk invariants of $L$ in framing $A$, with expansion

$$W_\Gamma^{(A)}(x_1,\ldots,x_g)=\sum_{d\in\mathbb{Z}_{\geq 0}^g\setminus\{0\}}n_d^{(A)}\operatorname{Li}_2(x^d),$$

where

$$\operatorname{Li}_2(x)=\sum_{n\geq 0}\frac{x^n}{n^2}$$

and $n_d^{(A)}$ are integers. This conjecture extends the Ooguri–Vafa, Aganagic–Vafa, and Aganagic–Klemm–Vafa disk-counting framework to the chromatic Lagrangian setting; a rigorous definition of the relevant open Gromov–Witten invariants remains in development.