The higher-rank replacement for property T in lattice cohomology

Let $G$ be a connected semisimple Lie group with finite center and without compact factors, and let $\tau$ denote the property T assumption in Theorem~. Higher-rank replacement conjecture. Theorem~ should remain true when $\tau$ is replaced by

$$\operatorname{rank}(G)\geq 2.$$

This would extend the theorem from groups with property T to all groups of rank at least two; the paper presents it as a possible strengthening, and no resolution is supplied here.