Boundary-case nonexplosivity conjecture for the coarse-grained model

Let $N$ be the model described in the preceding proposition, with parameters $\alpha$ and $p$ satisfying $\alpha=\log(1/p)$. Boundary-case nonexplosivity conjecture. The model $N$ is not explosive. The preceding argument proves nonexplosivity below this parameter threshold, while the boundary case is expected to require a substantially different Lyapunov argument.