Belkhechine–Bouaziz–Boudabbous–Pouzet conjecture for path-reversed tournaments

Let $Q_n$ be the tournament on $[n]=\{1,\ldots,n\}$ obtained from the natural transitive tournament by reversing precisely the consecutive pairs $12,23,\ldots,(n-1)n$. Equivalently, for $i<j$, orient $i\to j$ when $j\geq i+2$, and orient $i+1\to i$ when $j=i+1$. Here $\operatorname{inv}(D)$ denotes the minimum size of a family of vertex-set inversions whose application produces an acyclic, equivalently transitive, tournament. Belkhechine–Bouaziz–Boudabbous–Pouzet conjecture. The inversion number of $Q_n$ is

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

This conjecture concerns the exact number of induced subtournament reversals needed to make the structured tournament $Q_n$ transitive. The supplied source does not state its resolution; the status is therefore left open.