Linear-growth conjecture for the critical annihilating Pool model

Consider the annihilating version of the Pool model, in which excess particles at an attached location are annihilated, and take the particle density at criticality, $\lambda=1$. Critical annihilating Pool-model conjecture. The annihilating Pool model at criticality grows at a linear speed. The subcritical growth proof is expected to be robust for this variant, but its behavior at criticality remains open.