General sequence list-irregularity-strength conjecture

Let $G$ be a graph with no component isomorphic to $K_2$. For each degree $i$, let $n_i$ be the number of vertices of degree $i$, let $\Delta(G)$ be the maximum degree, and define

$$M_G=\operatorname{max}\{\lceil n_i^{1/i}\rceil:1\leq i\leq\Delta(G)\}.$$

The general sequence list-irregularity strength $\operatorname{ls}_\sigma^e(G)$ is the least $k$ such that, for every ordering of $E(G)$ and every assignment of lists of size $k$ to the edges, some edge list-weighting gives every vertex a distinct induced sequence of incident edge weights. The general sequence list-irregularity-strength conjecture. If $G$ is nice, then

$$\operatorname{ls}_\sigma^e(G)=M_G.$$

This is the list version of the preceding counting-bound conjecture and would make the same degree-counting lower bound sufficient even for arbitrary edge lists and edge orderings. The source gives no evidence that it has been resolved.