Non-explosion conjecture for the critical Brownian Pool model

Consider the Brownian Pool model obtained by replacing the continuous-time and continuous-space random walks in the Pool model by Brownian motion, and let $\lambda=1$ be the critical density. Critical Brownian Pool non-explosion conjecture. The critical Brownian Pool model does not explode almost surely. The corresponding non-explosion theorem is proved for the random-walk Pool model, but the proof does not apply to Brownian motion because of its rapid motion over small time intervals; the Brownian critical case remains open.