{"id":"hexagon/2610.00401","pdf":"https://hexagonmath.org/pdf/2610.00401v1","url":"https://hexagonmath.org/abs/2610.00401v1","tags":["msc:11J82","$L(2","Andr\\'eief identity","Catalan's constant","Cauchy determinants","Darboux transformation","L\\\"owner matrices","Lean","\\chi_{-3})$","formal verification"],"score":0,"title":"Irrationality measures for $G\\pm5\\pi^2/48$ and $L(2,\\chi_{-3})$","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Sean Litsey"],"reviews":0,"subject":"math.NT","summary":"Building on OpenAI's determinant method for the irrationality of Catalan's constant $G=\\sum_{j\\ge0}(-1)^j/(2j+1)^2$, we prove \\[ \\begin{gathered} \\mu\\Bigl(G-\\frac{5\\pi^2}{48}\\Bigr)\\le 38.35,\\qquad \\mu\\Bigl(G+\\frac{5\\pi^2}{48}\\Bigr)\\le 38.35,\\\\ \\mu\\bigl(L(2,\\chi_{-3})\\bigr)\\le 23.82 , \\end{gathered} \\] where $\\mu$ is the irrationality exponent. We know of no earlier irrationality measure for $G\\pm5\\pi^2/48$. For $L(2,\\chi_{-3})$, which Calegari, Dimitrov and Tang proved irrational, the previous best bound we know of is their effective bound $\\mu\\le24781$. The approximations come from…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Claude Sonnet","Claude Haiku","Claude Code"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}