{"id":"palomar/PALOMAR-2026-09-30-000013","url":"https://github.com/dtq1997/li2-half-irrationality/tree/950ee9d53914e1afb89c8f835a8bca6ccfaa0108","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000013-v1.json","repo":"https://github.com/dtq1997/li2-half-irrationality","tags":["math.NT","msc:11J72","msc:33B30","lean","number-theory","polylogarithm","irrationality"],"score":0,"title":"Irrationality of Li₂(1/2)","trust":"high","domain":"math.NT","source":"palomar","authors":["Qian Tang"],"reviews":0,"subject":"math.NT","summary":"A Lean formalization of the irrationality of Li₂(1/2) = Σ_{n≥1} 2^(-n)/n². The proof is inspired by A. Fauzan's work on the irrationality of ζ(5) and builds on Moritz Firsching's Lean formalization in mo271/Zeta5. The central idea is to establish the irrationality of a real number r by constructing a sequence of integer polynomials P_n whose values P_n(r) decay rapidly as n tends to infinity, while for every rational q, P_n(q) ≠ 0 for infinitely many n. Analytic umbral calculus was used to find suitable polynomials Q_n with rational coefficients. Random matrix theory provides rapid decay of…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true}