Qin's Euler partition-function conjecture for moduli spaces of curves

Let $X$) be a smooth projective complex variety. Let $\mathfrak I_n(X,\beta)$ be the moduli space of $1$-dimensional closed subschemes $Z$ of $X$ satisfying the paper's fixed numerical condition, and let $X^{[n]}=\mathfrak I_n(X,0)$ be the Hilbert scheme of length-$n$ $0$-dimensional closed subschemes of $X$. Qin's Euler partition-function conjecture. The reduced partition function for the Euler numbers

$$\frac{\sum_n\chi\bigl(\mathfrak I_n(X,\beta)\bigr)q^n}{\sum_n\chi\bigl(X^{[n]}\bigr)q^n}$$

is a rational function of $q$, and is invariant under $q\to 1/q$ when $K_X=0$. This is proposed as an analogue for Euler numbers of the Donaldson–Thomas conjecture that reduced partition functions are rational and, in the Calabi–Yau case, invariant under $q\to1/q$; the paper does not provide a resolution of this analogue.