Rationality conjecture for Weil–Petersson characteristic integrals

Let $M$ be a Weil–Petersson variety, and let $X$ be a Weil–Petersson subvariety of dimension $q$ in $M$. Let $c_k(\omega_{WP})$ denote the $k$-th elementary polynomial of the curvature tensor of the Weil–Petersson metric, and let $l$ satisfy $k+l=q$. Rationality conjecture. The characteristic integral

$$\int_X c_k(\omega_{WP})\wedge\omega_{WP}^l$$

is a rational number. This is proposed as a generalization of the rationality results for integrals involving the Weil–Petersson curvature and metric on the ambient variety; the source does not establish the claim in this generality.