The projective-space systolic conjecture for reversible optical hypersurfaces

Let $\Sigma$ be a reversible optical hypersurface in the cotangent bundle $T^*\mathbb{R}P^n$ of real projective $n$-space, enclosing a volume $V$. A periodic characteristic on $\Sigma$ is a closed characteristic of the induced contact structure. Projective-space systolic conjecture. The hypersurface $\Sigma$ carries a periodic characteristic whose action is at most

$$\frac{\sqrt[n]{V}}{2},$$

and this short characteristic can be chosen so that its projection onto the base manifold is a non-contractible loop. This is described as a generalization of the conjectured systolic optimality of the canonical metric in real projective spaces; the source gives no resolution status.