Differential geometry·OpenAI Math·Result 340
A counterexample to the nearby Lagrangian conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under differential geometry: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
A counterexample to the nearby Lagrangian conjecture
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What OpenAI claims
Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even N, constructs a closed exact embedded Lagrangian in T*(S9× SN-1) that is diffeomorphic to the base but not Hamiltonian isotopic to its zero section.
Paper
A counterexample to the nearby Lagrangian conjecture
We disprove the unrestricted nearby Lagrangian conjecture. For some sufficiently large even integer N, we construct a closed exact smoothly embedded Lagrangian in T*(S9× SN-1) that is diffeomorphic to the base but is not Hamiltonian isotopic to the zero section.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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