Minimum number of empty triangles in simple drawings of K_n

Prove that, for every n, the minimum number of empty triangles in any simple drawing of the complete graph K_n equals 2n−4.

Background

It is known that generalized twisted drawings of K_n always have exactly 2n−4 empty triangles, and they currently represent the largest class for which this exact count has been established. This number is widely believed to be the minimum across all simple drawings of K_n.

Establishing the general minimum would confirm a central conjecture in the study of empty triangles in simple drawings and further clarify the structural extremal properties of such drawings.