RIS and ARIS asymptotic finite-time average-consensus conjecture

Let $C_{[0,t_1]}$ be a communication sequence satisfying the $\mathrm{S\mathcal{V}SC}$ condition. Let the RIS algorithm be the algorithm proposed by Shah and Hassibi (2008), let the ARIS algorithm be the algorithm defined by the stated equations, and let $r$ be its positive integer parameter. RIS–ARIS conjecture. Both the RIS and ARIS algorithms imply average-consensus at time $t=t_1(+)$ almost surely in the limit as $r$ approaches infinity. This conjecture predicts asymptotic exactness of the two randomized algorithms under the stated communication condition; the supplied text gives no resolution.