The torsion conjecture for stabilizer abelianizations of groups of finite type

Let $G$ be a group of finite type of depth $D$. The quotient

$$\operatorname{St}_G(D-1)/\overline{\operatorname{St}_G(D-1)'}$$

is the abelianization of the level-$D-1$ stabilizer, where $\operatorname{St}_G(D-1)$ denotes the subgroup fixing all vertices at level $D-1$.

Torsion conjecture. The quotient

$$\operatorname{St}_G(D-1)/\overline{\operatorname{St}_G(D-1)'}$$

is torsion. In particular, the equivalence of just-infiniteness, topological finite generation, and strong completeness holds for all groups of finite type.

This condition is known for many groups of finite type and would extend the stated equivalence theorem from the groups satisfying the torsion hypothesis to all groups of finite type. The source states that a proof is not currently known.