{"id":"hexagon/2610.00590","pdf":"https://hexagonmath.org/pdf/2610.00590v1","url":"https://hexagonmath.org/abs/2610.00590v1","tags":["msc:60F99"],"score":0,"title":"The sharp iid Berry–Esseen inequality: Analytic reductions and exact certificate proof","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Kacper Rodziewicz","Bartosz Kołodziejek"],"reviews":0,"subject":"math.PR","summary":"Let $X_1, X_2, \\dots$ be independent and identically distributed real random variables with $\\mathbb{E}[X_1] = 0$, $\\mathbb{E}[X_1^2] = 1$, and finite third absolute moment $\\rho = \\mathbb{E}|X_1|^3 < \\infty$. Write $F_n(x) = \\mathbb{P}((X_1 + \\cdots + X_n)/\\sqrt{n} \\le x)$ and let $\\Phi$ denote the standard normal distribution function. Define \\[ \\Delta_n = \\sup_{x \\in \\mathbb{R}} |F_n(x) - \\Phi(x)|, \\qquad C_n = \\sup \\frac{\\sqrt{n}\\,\\Delta_n}{\\rho}, \\qquad C^* = \\sup_{n \\ge 1} C_n, \\] and let \\[ C_{\\mathrm{E}} = \\frac{3 + \\sqrt{10}}{6\\sqrt{2\\pi}} \\approx 0.4097321837 \\] denote Esseen's…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}