Remark: Family 340. A counterexample to the nearby Lagrangian conjecture

Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even $N$, constructs a closed exact embedded Lagrangian in $T^{\ast }(S^9\times S^{N-1})$ that is diffeomorphic to the base but not Hamiltonian isotopic to its zero section.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.