Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even N, constructs a closed exact embedded Lagrangian in T^*(S^9\times S^{N-1}) that is diffeomorphic to the base but not Hamiltonian isotopic to its zero section.
Manuscript
A counterexample to the nearby Lagrangian conjecture
September 23, 2026 · source · cite as \cite{OAI:A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026}
We disprove the unrestricted nearby Lagrangian conjecture. For some sufficiently large even integer N, we construct a closed exact smoothly embedded Lagrangian in T^*(S^9\times S^{N-1}) that is diffeomorphic to the base but is not Hamiltonian isotopic to the zero section.
Result 340 · Differential geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md