A new lower bound for the Schur-Siegel-Smyth trace problem

Abstract

We prove that lambda_SSS >= 1.80220 for the smallest limiting trace-to-degree ratio of totally positive algebraic integers, improving the bound 1.80203 obtained by Orloski, Talebizadeh Sardari and Smith. The proof exhibits an explicit probability measure on [0,8] together with eighteen integer polynomials, and verifies their dual inequality on the whole of [0,infinity) by interval bisection. The certificate assumes nothing about the data it is built from: an error in that data can only weaken the bound, never invalidate it.

arXiv comment5 pages. Ancillary files: the certificate (JSON) and two independent verification programs (Python, numpy and mpmath only)