Bounded denominator conjecture for stringy Euler numbers

Let $X$ be a $d$-dimensional algebraic variety with at worst Gorenstein canonical singularities. The bounded denominator conjecture asserts that the denominator of the rational number $e_{\rm st}(X)$ is bounded by a constant $C(d)$ depending only on $d$. This concerns the arithmetic behavior of stringy Euler numbers for singular varieties; the supplied text gives no resolution or further evidence for the claim.