{"id":"hexagon/2610.00338","pdf":"https://hexagonmath.org/pdf/2610.00338v1","url":"https://hexagonmath.org/abs/2610.00338v1","tags":["msc:11J81","msc:11J86","msc:14L10","msc:13C14","msc:68V20","Lean","formal verification","interpolation determinants","linear forms in logarithms","multiplicity estimates"],"score":0,"title":"A lean formalization of Roy's strong six exponentials theorem","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Shawn Krisman"],"reviews":0,"subject":"math.NT","summary":"We formalize in Lean 4 with Mathlib Roy's strong six exponentials theorem: if $x_1,x_2$ are linearly independent over $\\overline{\\mathbb{Q}}$ and $y_1,y_2,y_3$ are linearly independent over $\\overline{\\mathbb{Q}}$, then one of the six products $x_iy_j$ lies outside the $\\overline{\\mathbb{Q}}$-vector space spanned by $1$ and the logarithms of algebraic numbers. The proof closure uses only Lean's three standard axioms. Along the way the development proves Waldschmidt's transcendence theorem on $\\mathbb{G}_a^{d_0}\\times\\mathbb{G}_m^{d_1}$ in the form used by Roy, and Philippon's multiplicity…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-10-18","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}