AI 中文总结
本文通过显式概率测度与十八个整数多项式及区间二分法验证，将全正代数整数最小极限迹度比的下界从 1.80203 提升至 1.80220。
AI 中文摘要
我们证明全正代数整数的最小极限迹度比满足 lambda_SSS >= 1.80220，改进了 Orloski、Talebizadeh Sardari 和 Smith 得到的下界 1.80203。证明给出了 [0,8] 上的一个显式概率测度以及十八个整数多项式，并通过区间二分法在 [0,∞) 上验证它们的对偶不等式。该证书对其构建所依据的数据不作任何假设：数据中的错误只会削弱下界，而绝不会使其失效。
英文摘要
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.
Comments5 pages. Ancillary files: the certificate (JSON) and two independent verification programs (Python, numpy and mpmath only)
