Finite-time consensus for agents with memory

Let $V$ be the finite set of agents, let $X_v(t)$ be the estimator of agent $v$ at time $t$ in the model where agents retain their previous values, and let $X(\infty)$ denote the limiting estimator. Finite-time consensus conjecture.

$$\forall v\in V:\;X_v(t)=X(\infty),\qquad t\geq |V|.$$

The paper proves convergence to $Z(\infty)$ when agents have memory, and observes that agents accumulate additional estimators over time. It conjectures that this expanding span forces exact agreement by time $|V|$, but does not prove the finite-time assertion.