{"id":"openai-math/Uniform-Stability-of-the-Spherical-Laughlin-Gap","pdf":"https://github.com/openai/math/blob/main/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf","url":"https://github.com/openai/math/tree/main/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026","tags":["quantum-hall","spectral-gap","mathematical-physics","condensed-matter"],"score":0,"title":"Uniform Stability of the Spherical Laughlin Gap","domain":"Mathematical physics","family":"269","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove that the fermionic Laughlin V 1 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Uniform Laughlin gap and stability under bounded scalar disorder"}