The universal torsion conjecture for infinite-type Kac-Moody groups

Let $K(A)$ be a Kac-Moody group of infinite type, and let $G(A)$ denote the associated group. For a prime number $p$, consider the integral cohomology ring $H^*(BG(A);\mathbb Z)$. Universal torsion conjecture. For every prime $p$, the ring $H^*(BG(A);\mathbb Z)$ has $p$-torsion elements.

The claim extends the cited result of Ruan and Zhao for rank-$3$ infinite-type Kac-Moody groups. Its validity for arbitrary infinite-type Kac-Moody groups is left as an open conjecture in the source.