{"id":"hexagon/2610.00425","pdf":"https://hexagonmath.org/pdf/2610.00425v1","url":"https://hexagonmath.org/abs/2610.00425v1","tags":["math.OC","msc:11R06","msc:90C05","msc:65G30","Schur-Siegel-Smyth trace problem","ball arithmetic","computer-assisted proof","linear programming","totally positive algebraic integers"],"score":0,"title":"An explicit upper-bound certificate for the Schur–Siegel–Smyth trace constant","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Ricardo Pinho"],"reviews":0,"subject":"math.NT","summary":"We document an explicit certificate proving $C_{86}<1.8117251$ for the smallest limiting trace-to-degree ratio of totally positive algebraic integers. The construction uses the primal problem of Orloski and Talebizadeh Sardari, with their four-polynomial set enlarged to eleven. A discretised solution is rounded to a rational step density, then normalised to a probability measure. Exact rational calculations and rigorous ball-arithmetic inequalities verify Smith's sufficient criterion for an arithmetic measure. An independently written agent checker accepts the certificate and rejects four…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}