AI 中文总结
本研究通过显式证书将[0,1]的整数切比雪夫常数区间从1.39e-3缩小至4.56e-4，上界用92因子多项式，下界用947单元测度与206个多项式。
AI 中文摘要
自Pritsker（2005）和Flammang（2014）的工作以来，[0,1]的整数切比雪夫常数一直被界定在0.4213 <= t_Z([0,1]) <= 0.422685之间。我们证明了0.4222286000 <= t_Z([0,1]) <= 0.4226846975，将区间从1.39e-3缩小到4.56e-4。两个界均由显式证书确立。上界由一个具有92个因子和显式整数指数的整数多项式承载；下界由一个在947个单元上的离散测度以及206个不可约多项式的库，通过一个使可除性支付项显式化的不等式确立。两个自包含的脚本作为附件文件，仅凭证书即可重新推导出这两个界。
英文摘要
The integer Chebyshev constant of [0,1] has been bracketed by 0.4213 <= t_Z([0,1]) <= 0.422685 since the work of Pritsker (2005) and of Flammang (2014). We prove 0.4222286000 <= t_Z([0,1]) <= 0.4226846975, narrowing the interval from 1.39e-3 to 4.56e-4. Both bounds are established by explicit certificates. The upper bound is carried by an integer polynomial with 92 factors and explicit integer exponents; the lower bound by a discrete measure on 947 cells together with a library of 206 irreducible polynomials, through an inequality in which the terms paying for divisibility are made explicit. Two self-contained scripts, included as ancillary files, re-derive both bounds from the certificates alone.
Comments7 pages. Ancillary files: two certificates in JSON and two self-contained verification scripts (numpy and mpmath only). v2: corrects the numerical value of the improvement over the lower bound of [P05] in Section 1 (9.3e-4, not 9.1e-4); no change to any statement, proof, certificate or ancillary file
