{"id":"openai-math/A-Fock-space-inequality-and-the-Laughlin-spectral-gap","pdf":"https://github.com/openai/math/blob/main/preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026","tags":["quantum-hall","spectral-gap","fock-space"],"score":0,"title":"A Fock-space inequality and the Laughlin spectral gap","domain":"Mathematical physics","family":"269","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove the spherical fermionic Laughlin spectral-gap conjecture for the full V 1 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, $`H_Q^2\\ge\\gamma H_Q`$ for some fixed $`\\gamma\\gt 1/25`$ on the entire lowest-Landau-level Fock space for all sufficiently large flux Q , independently of particle number.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Uniform Laughlin gap and stability under bounded scalar disorder"}