The collinear-subset conjecture for minimum-diameter plane integral point sets

Let $n\ge 9$, and let a plane integral point set with minimum diameter be a plane integral point set of $n$ points whose diameter is minimal among such sets. A subset is collinear when all of its points lie on one line.

Collinear-subset conjecture. For $n\ge 9$, a plane integral point set with minimum diameter contains a subset of $n-1$ collinear points.

The paper proves this description for $9\le n\le 122$. The conjecture extends that computationally established range to all $n\ge 9$.