Birkhoff-section existence conjecture for nondegenerate Reeb vector fields

Let $M$ be a closed $3$-manifold and let $R$ be a nondegenerate Reeb vector field on $M$. A Birkhoff section is a surface with boundary whose interior is embedded and transverse to $R$, whose boundary is immersed and composed of periodic orbits, and which intersects every orbit of $R$ within bounded time. Birkhoff-section existence conjecture. Every nondegenerate Reeb vector field has a Birkhoff section. The source presents this as a conjecture, but the supplied context does not establish whether it is open or resolved.