Faudree–Lehel's irregularity-strength conjecture

Let $G$ be a $d$-regular graph on $n$ vertices with $d>1$. An irregular edge weighting assigns real weights to the edges so that all vertices have distinct weighted degrees, and $s(G)$ is the least $k$ for which an irregular weighting using weights from $\{1,2,\ldots,k\}$ exists. Faudree–Lehel's irregularity-strength conjecture. There is a constant $C>0$ such that, for every such graph,

$$s(G)\leq\frac{n}{d}+C.$$

The source says that this conjecture remains open, although its asymptotic validity has been confirmed. It is a central conjecture concerning irregularity strength.