Tightness is symplectically determined

Let $(Y,\xi)$ be a contact 3-manifold, and consider the half-symplectization $Y\times(-\infty,0]$ with symplectic form $d(e^t\alpha)$, where $\xi=\ker\alpha$. A compact properly embedded symplectic surface has fixed positive transverse boundary, and comparison surfaces are required to have the same relative homology class. Tightness is symplectically determined. The contact structure is tight if and only if every such compact properly embedded symplectic surface in half its symplectization maximizes Euler characteristic amongst all surfaces with the same relative homology class. This conjecture proposes a characterization of tightness using the symplectic geometry of the symplectization, extending the preceding result for contact structures with non-trivial Ozsváth–Szabó invariant.