Cichacz–Görlich–Tuza conjecture on cordial hypertrees

Let $H=(V,E)$ be a hypertree, meaning a connected hypergraph without cycles. A vertex labeling $f:V\to\mathbb{Z}_2$ induces an edge labeling by $f(e)=\sum_{v\in e}f(v)$ modulo $2$. The hypergraph is $2$-cordial when the numbers of vertices and edges receiving the two labels differ by at most $1$. Cichacz–Görlich–Tuza's conjecture. Every hypertree is $2$-cordial. The paper proves this statement, as part of the stronger result that every hypertree is $k$-cordial for $k\in\{2,3\}$.