The quarter-size upper-bound conjecture for crossing families of elbows

Let $S$ be a set of $n$ points in the plane in general position. An elbow is an orthogonal geometric-graph edge consisting of one horizontal and one vertical line segment, and a crossing family of elbows is a family in which every two elbows cross. Elbow crossing-family conjecture. There are point sets of $n$ elements that do not admit a crossing family of elbows with more than $\lfloor n/4\rfloor$ elements. The proved lower bound is $\lfloor n/4\rfloor$, while the matching upper-bound construction remains conjectural.