Weak-convergence conjecture for the bias voter model on trees and lattices

Let $\eta_t$ be the bias voter model on $S$, where $S=\mathbb{T}^d$ or $S=\mathbb{Z}^d$ with $d\geq 1$, started from the product initial distribution $\mu_p$ with $p\in (0,1)$. Weak-convergence conjecture. For any $\lambda>\theta$,

$$\eta_t\Rightarrow\delta_1$$

for $\{\eta_t\}_{t\geq 0}$ on $S$. This conjecture proposes that the weak convergence established in the paper for particular settings should hold under the generalized condition $\lambda>\theta$ on both regular trees and lattices. Its status is open in the supplied text.