OpenAI · 269-02 · 2026-09-24 · Mathematical physics
A Fock-space inequality and the Laughlin spectral gap
preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026
Family 269. The Laughlin gap and stability under scalar disorder.
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
Proves the fermionic Laughlin spectral-gap conjecture for the full interaction at filling on the round sphere. The unique ground state remains uniformly gapped under sufficiently weak bounded real scalar one-body potentials projected to the lowest Landau level. Both the gap and disorder threshold are uniform over all sufficiently large particle numbers and all normalized potential profiles.
We prove the spherical fermionic Laughlin spectral-gap conjecture for the full V1 interaction. With coefficient one for each pair projector, the gap above the Laughlin state at filling 1/3 on the round sphere is at least 1/25 for all sufficiently large systems. More generally, for some fixed on the entire lowest-Landau-level Fock space for all sufficiently large flux Q, independently of particle number.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 269: Uniform Laughlin gap and stability under bounded scalar disorder. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.