Asymptotic Gamma-class conjecture for monotone symplectic manifolds

Let $X$ be a monotone symplectic manifold. For Chern roots $x_j$ of $TX$, let $u$ be the equivariant parameter, let $J_X^d=ev^d_*\left(\frac{1}{1-u\psi}\right)$, and let $\langle J_X^d,\operatorname{Vol}_X\rangle_X$ denote the normalization appearing in the source. Asymptotic Gamma-class conjecture. One has

$$\lim_{d\to\infty}\left(\prod_{k=1}^{d}\prod_{j=1}^{\dim(X)}\left(1+\frac{x_j}{uk}\right)^{-1}-\frac{J_X^d}{\langle J_X^d,\operatorname{Vol}_X\rangle_X}\right)=0.$$

The convergence is faster than $O(\log(d)^{\dim(X)})$, in the sense stated in the source. This generalizes a termwise equality conjectured for Kähler varieties, while the source notes that only the limits agree for the twistor bundles under consideration; a general proof remains open.