The minimum codegree conjecture for spanning components in hypergraphs

Let $G$ be a $k$-graph on $n$ vertices, and let $\delta_{k-1}(G)$ denote its minimum $(k-1)$-degree. Minimum-codegree spanning-component conjecture. If

$$\delta_{k-1}(G) > n/k,$$

then $G$ contains a spanning component. This is a further open problem concerning connectivity under minimum codegree conditions, complementary to the minimum vertex-degree conjecture.