Conjectured unbounded imbalance for stretchable point configurations

For a finite set of points in the plane, consider every line determined by at least two points of the set, and compare the numbers of points on its two sides. Stretchable-configuration conjecture. There exists an unbounded function $f:\mathbb{N}\rightarrow\mathbb{N}$ such that, for every natural number $n$, there is a set of $n$ points for which the numbers of points on either side of each line determined by the set differ by at least $f(n)$. The paper's construction establishes the analogous phenomenon for pseudoline arrangements, while the stretchability of such configurations remains open; the conjecture proposes that configurations realizable by lines can also exhibit unbounded imbalance.