The uniform systole conjecture for arithmetic locally symmetric manifolds

Fix a symmetric space $S$ of non-compact type without Euclidean de Rham factors, and let an arithmetic $S$-manifold be a quotient $M=\Gamma\backslash S$ by a torsion-free arithmetic lattice. A closed geodesic is a periodic geodesic in $M$. The uniform arithmetic systole conjecture. There exists a constant $l=l(S)$ such that no arithmetic $S$-manifold contains a closed geodesic of length at most $l$. The claim would provide a uniform positive lower bound for the length of closed geodesics, equivalently a uniform lower bound for the injectivity radius in the compact case; the source derives it from Margulis's conjecture, so it remains open here.