Tight lower-bound conjecture for segregation in the Offended Voter Model

Let $q_N=q\in(0,1)$ be constant, let Z_0^{N,\textnormal{\min}}=\lfloor N/2\rfloor, and let $E^N\subset\mathbf{Z}^N_0$. Let $\mathcal{A}_N$ denote the segregation event, and let $\beta$ be the function appearing in the model's segregation lower bound. Tight-bound conjecture.

$$\lim_{N\to\infty}\mathbb{P}(\mathcal{A}_N)=\beta\left(\frac{q}{2(1-q)}\right).$$

The claim says that the lower bound established earlier is asymptotically exact. The paper motivates it by simulations showing close agreement for $N\geq1000$, but does not prove the required control of the coupled edge-deletion and opinion processes.