Subexponential end time conjecture for diffusion limited aggregation in the Boolean lattice

Let $t_{\mathrm{end}}$ denote the time at which the diffusion limited aggregation process reaches its terminal stage in the Boolean lattice on $n$ elements. Subexponential end time conjecture. The end time satisfies

$$t_{\mathrm{end}}=o(2^n).$$

The paper presents this as a likely consequence of empirical evidence, in the context of understanding the process between its beginning and end. No proof or resolution is provided here.