Critical Pool-model linear-growth conjecture

Let $\mathcal{E}_t$ denote the pool radius or size at time $t$ in the Pool model, and let $\lambda$ be the particle density. Critical Pool-model linear-growth conjecture. At the critical density $\lambda=1$, there exists $\xi>0$ such that

$$\lim_{t\to\infty}\frac{\mathcal{E}_t}{t}=\xi$$

almost surely. The theorem in the paper gives growth faster than every sublinear power at criticality, while the available upper bound is much weaker; the conjectured positive linear speed remains open.