发表机构
ShanghaiTech University（上海科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过计算机辅助方法结合奇 Hermite 阈值与相关多项式，证明实 Grothendieck 常数上界为 1.7813，优于现有文献值。
AI 中文摘要
我们给出一个计算机辅助证明，表明普遍实 Grothendieck 常数满足 $K_G^{\mathbb R}\le 1.7813$。该构造结合了一个显式的 11 次奇 Hermite 阈值和一个 51 次带符号相关多项式。通过将标量系数头部封闭到 301 次并利用加权高斯迹估计界定整个剩余尾部，验证了一个充分的反-主导不等式。有限积分在一个完整的区间划分上有界；其空间外部通过解析方法控制。精确参数和重新生成所有被接受的数值输入的源代码随论文附上。该界改进了近期文献中的显式界 $1.7818666069360661$ 以及随后报告的、经系统测试的值 $1.7813319810625639$。
英文摘要
We give a computer-assisted proof that the universal real Grothendieck constant satisfies $K_G^{\mathbb R}\le 1.7813$. The construction combines an explicit odd Hermite threshold of degree $11$ with a signed correlation polynomial of degree $51$. A sufficient inverse-majorant inequality is certified by enclosing the scalar coefficient head through degree $301$ and bounding the entire remaining tail using a weighted Gaussian trace estimate. The finite integral is bounded on a complete interval partition; its spatial exterior is controlled analytically. Exact parameters and source code that regenerate all accepted numerical inputs accompany the paper. The bound improves both the explicit bound $1.7818666069360661$ in the recent literature and the subsequently reported, system-tested value $1.7813319810625639$.
Comments9 pages
