Absolute rank gradient conjecture for lattices in higher-rank Lie groups

Let $\Gamma$ be a lattice in a higher-rank Lie group, and let its absolute rank gradient be the infimum of $(d(H)-1)/[\Gamma:H]$ over finite-index subgroups $H\leq\Gamma$, where $d(H)$ is the minimal number of generators of $H$. Absolute rank gradient conjecture. All lattices in higher-rank Lie groups have absolute rank gradient $0$. This would relate subgroup-generation growth in higher-rank lattices to measurable cost and fixed-price questions. The source presents the assertion as an unresolved question in that context.