Linear-time threshold for condensation in regime R3

Let $m(t)$ denote the time-dependent memory parameter in Regime $R3$, let $\mu_\epsilon$ be the mean of the fitness increments, and let the cumulative fitness distribution be the distribution of cumulative fitness values. Linear-threshold condensation conjecture in $R3$. If

$$m(t)=\Theta(t),$$

then Regime $R3$ exhibits condensation, with the cumulative fitness distribution having an atom at $\mu_\epsilon t$. The paper presents this as an open problem motivated by simulations and central-limit-theorem heuristics; the threshold and asserted atom are not proved in the supplied text.