Arnold's exact Lagrangian conjecture for cotangent bundles

Let $N$ be a compact closed manifold, and let $L\subset T^*N$ be a compact closed exact Lagrangian submanifold, where $T^*N$ has its standard Liouville form. Arnold's conjecture. $L$ is Hamiltonian isotopic to the zero section. The conjecture concerns the rigidity of exact Lagrangian submanifolds in cotangent bundles. A theorem of Fukaya–Seidel–Smith, Nadler–Zaslow, Abouzaid, and Kragh shows that a compact connected exact Lagrangian is quasi-isomorphic to the zero section in the wrapped Fukaya category and projects homotopy equivalently to $N$, but the stated Hamiltonian-isotopy conclusion remains open.