Kingston et al.'s synchronization conjecture for perimeter surveillance

A configuration consists of a time $t$ together with the positions, directions, and estimates of all drones at that time. A drone is left synchronized at time $t$ if thereafter it never goes to the left of its left endpoint, and right synchronized at time $t$ if thereafter it never goes to the right of its right endpoint. It is synchronized at time $t$ if it is both left and right synchronized. Kingston et al.'s synchronization conjecture. If all drones have correct estimates at time $t$, then all drones are synchronized by time $t+2$. This is a proposed finite-time synchronization property of the perimeter-surveillance algorithm. The surrounding discussion notes that the algorithmic arguments need formalization and that Zeno behavior must be ruled out, but gives no evidence resolving this conjecture.