Sandon's translated-points conjecture for contactomorphisms

Let $(V,\xi)$ be a closed contact manifold, where $\xi$ is a cooriented contact structure, and let $\operatorname{Cont}_0(V,\xi)$ denote the identity component of its contactomorphism group. Fix a contact form $\alpha$ with $\xi=\ker\alpha$. A point $x\in V$ is an $\alpha$-translated point of a contactomorphism $\phi$ if

$$\exists s\in\mathbb{R}\quad\text{such that}\quad \phi(x)=\phi_\alpha^s(x)\quad\text{and}\quad (\phi^*\alpha)_x=\alpha_x,$$

where $\{\phi_\alpha^t\}_{t\in\mathbb{R}}$ is the Reeb flow of $\alpha$. Sandon's translated-points conjecture. For every $\phi\in\operatorname{Cont}_0(V,\xi)$ and every contact form $\alpha$, the number of $\alpha$-translated points of $\phi$ is at least the number of critical points of a function. The conjecture predicts an analogue of the Arnold conjecture for contactomorphisms, replacing fixed points by translated points. The source does not specify the function or provide evidence resolving the conjecture, so its precise lower bound and status should be checked against the surrounding paper or cited literature.