Okounkov's multiple q-zeta value conjecture for Hilbert schemes of points

Let $X$ be a smooth projective surface, let $X^{[n]}$ be the Hilbert scheme of $n$ points on $X$, and let $L$ be a line bundle on $X$. For the reduced generating series $\big \langle {\rm ch}_{k_1}^{L}\cdots {\rm ch}_{k_N}^{L}\big \rangle'$ defined from the Chern characters of the tautological bundles and the total Chern classes of the tangent bundles of the Hilbert schemes, Okounkov's conjecture. The series $\big \langle {\rm ch}_{k_1}^{L}\cdots {\rm ch}_{k_N}^{L}\big \rangle'$ is a multiple $q$-zeta value of weight at most

$$\sum_{i=1}^N(k_i+2).$$

The conjecture concerns the arithmetic structure of Hilbert-scheme intersection generating series. Its resolution status is not specified in the supplied text.