Uniform Laughlin gap and stability under bounded scalar disorder

What OpenAI claims

Proves the fermionic Laughlin spectral-gap conjecture for the full V1 interaction at filling 1/3 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. (Lean)

Papers (2)

1. Uniform Stability of the Spherical Laughlin Gap

   5 October 2026 · Preprint, not peer reviewed · PDF

   We prove that the fermionic Laughlin V1 Hamiltonian at filling 1/3 on expanding round spheres retains a unique ground state and a uniform spectral gap under sufficiently weak bounded real scalar one-body potentials projected to the lowest Landau level. With coefficient one for each pair projector and Laughlin flux q=3(N-1), the gap and perturbation threshold are uniform for all sufficiently large particle numbers and all potential profiles of supremum norm at most one. The result uses the uniform unperturbed Fock-space gap and gives existential constants.

2. A Fock-space inequality and the Laughlin spectral gap

   24 September 2026 · Preprint, not peer reviewed · PDF

   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, H_Q² ≥ γ H_Q for some fixed γ > 1/25 on the entire lowest-Landau-level Fock space for all sufficiently large flux Q, independently of particle number.

Status

Preprint. The papers have 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.