Arnold-type cuplength conjecture for Lagrangian intersections

Let $(X,\omega)$ be a symplectic manifold, and let $L$ and $L'$ be Lagrangian submanifolds of $X$. Assume that $X$ is either closed or a Liouville manifold, and that $L$ is connected, closed, and relatively exact, meaning

$$\omega\cdot\pi_2(X,L)=0.$$

Write $\mathrm{Crit}(L)$ for the minimal number of critical points of any smooth map $L\to\mathbb{R}$. Arnold-type Lagrangian intersection conjecture. There is a lower bound

$$\#(L\cap L')\geq \mathrm{Crit}(L).$$

This is a nontransverse version of the Arnold conjecture for Lagrangian intersections. The transverse case admits lower bounds from Floer homology, while the stated bound is formulated under relative exactness to exclude disc and sphere bubbling.