Weak recovery threshold in the geometric block model

Let $\mathrm{GBM}(n,s,t)$ denote the geometric block model, and suppose it has a giant component. Weak recovery means recovering the communities with nontrivial accuracy by an efficient algorithm.

Weak recovery threshold conjecture. Let $s,t\geq 0$ and suppose $\mathrm{GBM}(n,s,t)$ has a giant component. Weak recovery is efficiently solvable in $\mathrm{GBM}(n,s,t)$ if and only if $s>0$.

This conjecture proposes that any positive geometric separation suffices for efficient weak recovery, provided a giant component exists. The source gives no resolution, so the claim remains open.