{"id":"hexagon/2610.00207","pdf":"https://hexagonmath.org/pdf/2610.00207v1","url":"https://hexagonmath.org/abs/2610.00207v1","tags":["math.CV","msc:11M26","C2 Function","Dirichlet Sums","Riemann Zeta Function"],"score":0,"title":"How long can an off-line zero survive the de Bruijn-Newman heat flow? An explicit unconditional lower bound for Lambda","domain":"math.NT","source":"hexagon","authors":["Pedro Caceres"],"reviews":0,"subject":"math.NT","summary":"Let $\\Lambda$ be the de Bruijn-Newman constant. The Riemann hypothesis (RH) is equivalent to $\\Lambda\\le 0$, and Rodgers and Tao proved $\\Lambda\\ge 0$. We ask how small $\\Lambda$ can be if $\\zeta$ has a zero $1/2+\\delta+i\\gamma$ with $\\delta>0$. We use de Bruijn's strip, the zero dynamics of the Polymath project, and an explicit local zero count for the heat-flow deformations $H_\\tau$ that we prove here. With these we show unconditionally that $\\Lambda \\ge \\delta^2/(70\\log\\gamma\\log\\log\\gamma)$. Equivalently, every zero $\\beta+i\\gamma$ of $\\zeta$ with $\\gamma\\ge 3\\cdot 10^{12}$ satisfies…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Python"],"discussed":0,"published":"2026-10-12","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}