Spanning tight components in 4-uniform hypergraphs

We prove that every $n$-vertex 4-uniform hypergraph with minimum codegree at least $\lfloor n\mathrm{/}4\rfloor$ has a spanning tight component. This is tight, and it settles the 4-uniform case of a conjecture of Illingworth, Lang, Müyesser, Parczyk, and Sgueglia.