Forbidden connected subsequences in bounded confidence processes

Let $(c_1,\dots,c_l)$ be a sequence of cluster sizes of a bounded confidence (BC) process. A subsequence is connected when its corresponding clusters are connected in the final configuration. Forbidden-subsequence conjecture. There cannot be a connected subsequence $(1,1,1,1)$ or $(2,2,1,1,1,2,2)$. This would constrain the possible cluster-size patterns and may help establish upper bounds on the number of connected components. The claim is presented as a conjecture, and no resolution is given in the source.