The four locally irregular subgraphs conjecture

Let $G=(V,E)$ be a connected graph, and let $\mathfrak{T}'$ be the family of connected graphs that are not decomposable into any number of locally irregular subgraphs. A graph is decomposable into $k$ locally irregular subgraphs if its edge set can be partitioned as $E=E_1\cup\cdots\cup E_k$ so that each spanning subgraph $(V,E_i)$ is locally irregular, meaning that adjacent vertices have distinct degrees.

Four-subgraph conjecture. Each connected graph $G$ which does not belong to $\mathfrak{T}'$ is decomposable to $4$ locally irregular subgraphs.

This is the less restrictive variant proposed after a connected exception to the three-subgraph conjecture was found. The source does not state a resolution of this four-subgraph variant.