Batyrev's stringy Chern-number conjecture

Let $\mathcal{X}$ be a Gorenstein proper Deligne–Mumford stack with projective coarse moduli space $X$, such that $\mathcal{X}\to X$ is proper and birational and $K_\mathcal{X}$ is the pullback of $K_X$. Let $c_{st}^{1,n-1}(X)$ be the stringy Chern number and let $II\mathcal{X}$ be the double inertia orbifold. Stringy Chern-number conjecture. One has

$$c_{st}^{1,n-1}(X)=\int_{II\mathcal{X}}c_1(T_\mathcal{X})c_{\operatorname{top}-1}(T_{II\mathcal{X}}).$$

This identity would identify the stringy Chern number with its orbifold characteristic-class counterpart and would imply the corresponding comparison needed for the orbifold Libgober–Wood formula. The paper notes that the equality is known in the Calabi–Yau case because both sides vanish there, but leaves the general case open.