Wang–Hu–Long's irrationally elliptic Reeb-orbit conjecture

Let $\Sigma^{2n-1}$ bound a convex domain in $\mathbb{R}^{2n}$, with $n\geq 2$, and let $\mathcal{T}(\Sigma)$ denote the set of prime closed Reeb orbits on $\Sigma$. A closed Reeb orbit is irrationally elliptic when its linearized return map decomposes into rotations whose rotation angles are irrational multiples of $\pi$. Wang–Hu–Long conjecture. If

$$\#\mathcal{T}(\Sigma)<\infty,$$

then all the closed Reeb orbits on $\Sigma$ are irrationally elliptic. This is known in dimension four and in several special higher-dimensional settings, but the general convex case remains open.