The inversion number of the tournament $Q_n$

Let $Q_n$ be the tournament obtained from the transitive tournament of order $n$ by reversing the arcs of its unique directed Hamiltonian path.

The $Q_n$ inversion-number conjecture.

$$\operatorname{inv}(Q_n)=\left\lfloor\frac{n-1}{2}\right\rfloor.$$

The source introduces this as the explicit-tournament motivation for Belkhechine et al.'s lower-bound conjecture. The source does not state a resolution.