The degenerate Arnol'd conjecture for Hamiltonian-isotopic Lagrangians

Let $(M,\omega)$ be a closed symplectic manifold, and let $L_0,L_1 a0M$ be a Hamiltonian-isotopic pair of Lagrangians. Suppose each $L_i$ is connected and closed, and satisfies

$$\omega\vert_{\pi_2(M,L_i)}=0.$$

Here $C^\infty(L_i)$ denotes the smooth real-valued functions on $L_i$, and $\operatorname{Crit}(f)$ is the set of critical points of $f$.

Degenerate Arnol'd conjecture. The intersection satisfies

$$\lvert L_0\cap L_1\rvert\geq\min\big\{\lvert\operatorname{Crit}(f)\rvert:f\in C^\infty(L_i)\big\}.$$

This is a lower bound for possibly degenerate Lagrangian intersections, motivated by Floer homotopy theory and intended to strengthen intersection bounds in settings such as plumbings of cotangent bundles. The supplied text gives no evidence that this conjecture has been resolved.