{"id":"hexagon/2610.00398","pdf":"https://hexagonmath.org/pdf/2610.00398v2","url":"https://hexagonmath.org/abs/2610.00398v2","tags":["cs.LO","msc:11J81","msc:11J86","msc:11J61","msc:68V20","Lean 4","Mathlib","formal verification","interpolation determinants","linear forms in logarithms"],"score":0,"title":"$\\log_p 2 \\cdot \\log_p(3+\\sqrt2)$ is not a $p$-adic linear form in logarithms","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Shawn Krisman"],"reviews":0,"subject":"math.NT","summary":"Let $p$ be a prime, $\\mathbb{C}_p$ the completion of an algebraic closure of $\\mathbb{Q}_p$, $\\overline{\\mathbb{Q}}$ the algebraic numbers in $\\mathbb{C}_p$, $L$ the $\\mathbb{Q}$-vector space of $p$-adic logarithms of algebraic numbers, and $\\mathcal{L}=\\overline{\\mathbb{Q}}+\\overline{\\mathbb{Q}}L$ the space of $p$-adic linear forms in logarithms of algebraic numbers with algebraic coefficients. We prove, in Lean 4 with Mathlib and from the three standard axioms only, that $\\log_p 2\\cdot\\log_p(3+\\sqrt2)\\notin\\mathcal{L}$ for every prime $p\\equiv\\pm3 \\pmod 8$, together with a family of…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Fable"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}