Lexicographically least extremal permutation conjecture

Let $n>2$ be prime, and define a permutation $g$ of $\mathbb Z_n$ by

$$g(x)=\begin{cases}x/(x-1)&\text{if }x\neq1,\\1&\text{if }x=1. \end{cases}$$

Order permutations lexicographically, and let $\Psi(n)$ be the minimum number of collinear triples in a permutation graph. Lexicographically least extremal permutation conjecture. The function $g$ is the lexicographic-least permutation with $(n-1)/2$ collinear triples for $n>2$ prime. The source presents this as a conjectural statement following the conjecture that $\Psi(n)=(n-1)/2$ and supplies no proof or resolution.