Neuhauser–Pacala coexistence conjecture for the symmetric model

Let the symmetric Neuhauser–Pacala model be the competing-species system on the lattice $\mathbb Z^d$, with coexistence meaning that both species persist in the long term. Neuhauser–Pacala coexistence conjecture. There is coexistence in the symmetric Neuhauser–Pacala model on $\mathbb Z^d$ for any $d\geq 2$. This conjecture is related to questions about invariant distributions and limiting distributions for the model; its full resolution is not stated here.