The specific sequence irregularity strength conjecture

Let $G$ be a graph without a component isomorphic to $K_2$. For each $1\le i\le\Delta(G)$, let $n_i$ be the number of vertices of degree $i$, and define

$$M_G=\max\left\{\left\lceil\sqrt[i]{n_i}\right\rceil:1\le i\le\Delta(G)\right\}.$$

The specific sequence irregularity strength conjecture. The specific sequence irregularity strength of $G$ is equal to $M_G$.

Specific sequence irregularity strength asks for the existence of an ordering of $E(G)$ for which an edge coloring induces distinct color sequences at all vertices. The paper presents this as a weaker conjecture after refuting the general version, and no resolution is supplied here.