Erdős–Sós bipartite-links conjecture for 3-graphs

A 3-graph is a 3-uniform hypergraph, and the link graph of a vertex is the graph whose vertices are the remaining vertices, with an edge for each 3-edge containing the given vertex. Let $\pi($odd cycle in link graph$)$ denote the maximum possible asymptotic edge density of a 3-graph whose link graphs contain no odd cycle, equivalently are bipartite. Erdős–Sós conjecture.

$$\pi(\operatorname{odd\ cycle\ in\ link\ graph})=1/4.$$

This is the bipartite-links problem for 3-graphs; the source presents it as a conjecture of Erdős and Sós and does not indicate a resolution.