Eisenstein homology conjecture for S-arithmetic groups

Let $T$ be a finite set of primes with $|T|=d$, and let $Y(K[1/T])$ be the associated $S$-arithmetic space. Eisenstein homology conjecture. Then $H_i(Y(K[1/T]),\mathbf{Z})$ is Eisenstein for every $i\leq d$; equivalently,

$$H^i(Y(K[1/T]),\mathbf{Q}/\mathbf{Z})$$

is Eisenstein for every $i\leq d$. This conjecture controls low-degree cohomology of $S$-arithmetic groups and is known in degree $1$ whenever the congruence subgroup property is available, while higher degrees are related to $K$-theoretic classes.