The weak 3-weighting conjecture for uniform hypergraphs

Let $H=(V,E)$ be an $r$-uniform hypergraph without isolated edges, where $r\geq 3$. A weight function is a map $\omega:E\to\{1,2,3\}$, inducing the vertex-coloring $c:V\to\mathbb{N}$ by

$$c(v)=\sum_{e\ni v}\omega(e).$$

The coloring is weak if no edge is monochromatic, and $H$ is weakly 3-weighted if some such weight function induces a weak coloring.

Weak 3-weighting conjecture. For each $r\geq 3$, every $r$-uniform hypergraph without isolated edges is weakly 3-weighted.

This extends the graph 1-2-3 conjecture to uniform hypergraphs and strengthens the previously mentioned weak weighting results. The claim is presented as an open belief in the source, with no resolution supplied.