An explicit upper-bound certificate for the Schur–Siegel–Smyth trace constant
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…
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