Erdős's conjecture on the first unresolved triangle count

Let $F(t)$ denote the maximum number of points that can be placed in the plane while determining exactly $t$ distinct triangles.

Erdős's conjecture. Any set of seven points in the plane determines at least four distinct triangles; consequently,

$$F(3)=6.$$

The paper proves the corresponding optimal values for one and two distinct triangles and identifies configurations attaining them. The asserted seven-point lower bound, and hence the value $F(3)=6$, is presented as an open conjecture.