Minimum vertex degree threshold for $C_4^3$-tiling

We prove that the vertex degree threshold for tiling ${\text{C}}_4^3$ (the 3-uniform hypergraph with four vertices and two triples) in a 3-uniform hypergraph on $n\in 4\mathbb{N}$ vertices is $\left(\genfrac{}{}{0px}{}{n-1}{2}\right)-\left(\genfrac{}{}{0px}{}{\frac{3}{4}n}{2}\right)+\frac{3}{8}n+c$, where $c=1$ if $n\in 8\mathbb{N}$ and $c=-\frac{1}{2}$ otherwise. This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling.