{"id":"hexagon/2610.00147","pdf":"https://hexagonmath.org/pdf/2610.00147v3","url":"https://hexagonmath.org/abs/2610.00147v3","tags":["stat.TH","msc:60F99"],"score":0,"title":"Moment defects and sharp iid Berry–Esseen bounds","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Kacper Rodziewicz","Bartosz Kołodziejek"],"reviews":0,"subject":"math.PR","summary":"Starting from Shevtsova’s sharp third-moment inequality, we develop an exact defect from the standardized two-point family and derive quantitative transport and characteristic-function bounds. A penalized extremal problem yields eventual two-point optimality, \\(C_n=C_Q^*(n)<C_{\\mathrm E}\\), together with a uniform linear deficit and sharp cubic Wasserstein stability. A fifth-order lattice saddle-point expansion gives the full oscillatory \\(n^{-2}\\) correction to the optimal constants. A separate effective argument proves \\(C_n<C_{\\mathrm E}\\) for every \\(n\\ge31\\), using finite-index…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-07","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}