2-cordiality conjecture for 1-degenerate connected hypergraphs

Let $H$ be a connected hypergraph. It is $1$-degenerated if every subhypergraph of $H$ has a vertex of degree at most $1$. A hypergraph is $2$-cordial when a labeling of its vertices by $\mathbb{Z}_2$, with each edge labeled by the sum modulo $2$ of the labels of its vertices, makes the numbers of vertices and edges receiving the two labels differ by at most $1$. 1-degenerate hypergraph cordiality conjecture. Every $1$-degenerated connected hypergraph is $2$-cordial. The paper identifies this as a natural next step beyond its proof that all hypertrees are $2$-cordial; its status is left open.