Weierstrass quantum-curve conjecture

Consider the Weierstrass spectral curve

$$P(x,y)=y^2-4(x^3-1)=0.$$

Let $\hat{P}(\hat{x},\hat{y};\hbar)$ be a quantum curve of the form

$$\hat{P}(\hat{x},\hat{y};\hbar)=\hbar^2\frac{\mathrm{d}^2}{\mathrm{d}x^2}-4(x^3-1)+\sum_{i\geq 1}\hbar^{2i}A_{2i}(x)\frac{\mathrm{d}}{\mathrm{d}x}+\sum_{j\geq 1}\hbar^{2j}B_{2j}(x),$$

where the $A_i(x)$ and $B_j(x)$ are polynomials in $x$. A Weierstrass quantum-curve conjecture. There is a unique such quantum curve that annihilates the non-perturbative wave-function:

$$\hat{P}(\hat{x},\hat{y};\hbar)\psi_{\mathrm{NP}}(z)=0.$$

Only even powers of $\hbar$ occur; moreover, $A_{2i}(x)$ has degree at most $i-2$, and $B_{2j}(x)$ has degree at most $j$. This conjecture concerns whether the non-perturbative wave-function for the Weierstrass spectral curve is annihilated by a uniquely determined quantum curve of the specified polynomial form. Its status is not resolved in the source.