Kiyota–Murai–Wada rationality conjecture for Cartan matrix eigenvalues

Let $B$ be a block of a finite group $G$ over an algebraically closed field of characteristic $p>0$, let $C\in\mathbb{Z}^{l\times l}$ be its Cartan matrix, and let $D$ be a defect group of $B$. Write $ED$ for the multiset of elementary divisors of $C$, $EV$ for the multiset of eigenvalues of $C$, and let $\rho(C)$ denote the spectral radius of $C$. Kiyota–Murai–Wada conjecture. The following assertions are equivalent: $EV=ED$; $\rho(C)=|D|$; $\rho(C)\in\mathbb{Z}$; and $EV\subseteq\mathbb{Z}$. The conjecture is known for blocks of finite or tame representation type, for $p$-solvable groups, and when $D\unlhd G$, but the stated equivalence is false in general: the principal $5$-block of $\operatorname{PSU}(3,4)$ has $\rho(C)=|D|$ while $EV\ne ED$.