Randomized DDA average-consensus conjecture under condition (C)

Let $C_{[0,t_1]}$ be a communication sequence, and let the $\mathrm{S\mathcal{V}CC}$ condition be defined by condition (C) of the cited theorem. Upon reception of each signal, choose the normal consensus-estimate update with probability $p\in(0,1)$ and the alternative update with probability $1-p$. Randomized DDA conjecture. Under these assumptions, average-consensus holds at time $t=t_1(+)$ almost surely for every communication sequence $C_{[0,t_1]}$ satisfying the $\mathrm{I\mathcal{V}CC}$ condition. The conjecture proposes that random switching between the two global updates restores finite-time average consensus under the broader condition (C); the supplied text gives no resolution.