Existence conjecture for optimal extended irregular dominating labelings of cycles

Let $C_{4n}$ be the cycle on $4n$ vertices, and let an optimal extended irregular dominating labeling mean a labeling satisfying the paper's extended irregular domination conditions with the minimum possible number of labeled vertices. Cycle-labeling conjecture. There exists an optimal extended irregular dominating labeling for $C_{4n}$ for every $n\geq 3$. The cases $n=1,2$ are known exceptions, and the source gives examples for $3\leq n\leq 6$; existence beyond these checked cases remains open.