Resource-cost lower bound for finite-time average-consensus algorithms

Let $\mathcal{A}$ be a distributed algorithm, let $C_{[0,t_1]}$ be a communication sequence, and let $\mathrm{S\mathcal{V}SC}$ denote the relevant sufficient vertex-strongly-connected condition. Let (P) be the knowledge-set property described in the preceding discussion, and let $O(nd)$ denote the stated asymptotic resource bound. Resource-cost conjecture. If $\mathcal{A}$ guarantees average-consensus at time $t=t_1(+)$ for every communication sequence $C_{[0,t_1]}$ satisfying the $\mathrm{S\mathcal{V}SC}$ condition, then $\mathcal{A}$ must have resource costs at least as great as those of any algorithm satisfying (P). In particular, such an algorithm requires that a set with cardinality upper bounded by at least $O(nd)$ can be communicated and stored at each node. This conjecture asserts a lower bound on the communication and storage resources needed for finite-time average consensus under the stated communication condition; the supplied text gives no resolution.