Short Geodesic Conjecture for arithmetic hyperbolic orbifolds

Let an arithmetic hyperbolic orbifold of the first type be a quotient of hyperbolic space by an arithmetic lattice of the first type. For a hyperbolic element $\gamma$, write $\ell(\gamma)$ for the length of its associated closed geodesic. Short Geodesic Conjecture. There exists a positive universal lower bound on the length of geodesics in an arithmetic hyperbolic orbifold of the first type. Through the relationship $\lambda=e^{\ell(\gamma)}$ between geodesic lengths and Salem numbers, this is presented as a reformulation of Lehmer's conjecture. The source does not provide evidence resolving the conjecture.