OpenAI · 340-01 · 2026-09-23 · Differential geometry
A counterexample to the nearby Lagrangian conjecture
preprints/A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026
Family 340. A counterexample to the nearby Lagrangian conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even , constructs a closed exact embedded Lagrangian in that is diffeomorphic to the base but not Hamiltonian isotopic to its zero section.
We disprove the unrestricted nearby Lagrangian conjecture. For some sufficiently large even integer N, we construct a closed exact smoothly embedded Lagrangian in that is diffeomorphic to the base but is not Hamiltonian isotopic to the zero section.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.