The superlinear blocking conjecture for general-position planar point sets

For a finite set $P$ of points in the plane, a set $B$ of points disjoint from $P$ blocks $P$ if every segment joining two distinct points of $P$ contains a point of $B$. If $P$ is in general position, let $b(P)$ be the minimum size of a blocking set for $P$, and let $b(n)$ be the minimum of $b(P)$ over all $n$-point sets in general position. Superlinear blocking conjecture. The minimum blocking number satisfies

$$\frac{b(n)}{n}\rightarrow\infty\quad\text{as }n\rightarrow\infty.$$

This asserts that every general-position point set requires superlinearly many blockers; Pinchasi conjectured the stronger bound $b(n)\in\Omega(n\log n)$.