The spectral meta-algorithm is optimally accurate in the geometric block model

Let $\mathrm{GBM}(n,s,t)$ be the geometric block model and suppose it has a giant component. Let $\delta$ denote an accuracy level, and let the spectral meta-algorithm be the algorithm described in the source.

Spectral meta-algorithm conjecture. For any $s$ and $r$ such that $\mathrm{GBM}(n,s,t)$ has a giant component, there exists $\delta>1/2$ such that the spectral meta-algorithm recovers communities with accuracy $\delta$ on $\mathrm{GBM}(n,s,t)$, and no algorithm recovers communities with accuracy $\delta+\Omega(1)$ on $\mathrm{GBM}(n,s,t)$.

The claim is intended to say that the spectral meta-algorithm attains optimal accuracy in the geometric block model. The source gives no resolution. The statement has an apparent parameter mismatch, mentioning $r$ while using $t$ in the model.