Asymptotic J-function conjecture for monotone symplectic manifolds

Let $X$ be a monotone symplectic manifold, let $J_X^d$ be the degree-$d$ contribution defined by $J_X^d=ev^d_*\left(\frac{1}{1-u\psi}\right)$, and let

$$J_X=e^{\frac{\log(t)c_1}{u}}\sum_d t^{c_1(d)}J_X^d.$$

Asymptotic J-function conjecture. One has

$$\lim_{t\to\infty}\frac{J_X}{\langle J_X,\operatorname{Vol}_X\rangle_X}=\lim_{d\to\infty}\frac{e^{\frac{c_1\log(d)}{u}}J_X^d}{\langle J_X^d,\operatorname{Vol}_X\rangle_X}.$$

This relates the large-parameter asymptotics of the full J-function to those of its individual degree contributions. The source gives no evidence that the conjecture has been proved or refuted.