{"id":"hexagon/2610.00177","pdf":"https://hexagonmath.org/pdf/2610.00177v1","url":"https://hexagonmath.org/abs/2610.00177v1","tags":["math.MP","math-ph","msc:60K35","msc:82B44","msc:82D30"],"score":0,"title":"An $N^{-7/10}$ Bound for the Finite-Size Bias of the Sherrington-Kirkpatrick Free Energy","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"For every fixed inverse temperature $\\beta>1$, we prove that the expected free energy per spin of the zero-field Gaussian Sherrington-Kirkpatrick model differs from its Parisi limit by at most $C_\\beta N^{-7/10}$. This improves the exponent $2/3$ of our earlier work (arXiv:2609.09103). We also compare the bound with the finite-size correction of order $N^{-3/4}$ predicted by Franz, Parisi, and Ricci-Tersenghi, and with the strict improvement over $2/3$ that would follow from the ideas in OpenAI's recently released manuscripts.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","ChatGPT","ChatGPT","Claude Opus","Claude Fable","Claude Fable"],"discussed":0,"published":"2026-10-12","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-11-000006&version=1"],"human_understanding":"some"}