发表机构
USC; UC Davis; Bocconi University（南加州大学; 加州大学戴维斯分校; 博科尼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过原始/对偶搜索与AI认证，确定实Grothendieck常数$K_G$的百分位，证明$1.773 \leq K_G \leq 1.7799$，并估计$K_G \approx 1.779$。
AI 中文摘要
我们通过证明 $1.773 \leq K_G \leq 1.7799$ 确定了实 Grothendieck 常数的百分位数字。此外，数值启发式方法表明估计 $K_G \approx 1.779$。我们首先简化了基于 Hermite 投影博弈和 Krivine 舍入方案的 $K_G$ 高斯对偶理论。这些界限是通过对这些对象进行启发式原始/对偶搜索获得的，随后对其值进行严格的 {\bf 认证}。搜索和认证使用 AI 工具执行，特别是严格的证书非常大（解析化简为数千个数值不等式）。
英文摘要
We determine the hundredths digit of the real Grothendieck constant by proving $1.773 \leq K_G \leq 1.7799$. Furthermore, numerical heuristics suggest the estimate $K_G \approx 1.779$. We start by simplifying the Gaussian duality theory of $K_G$, based on Hermite projection games and Krivine rounding schemes. The bounds are obtained by a heuristic primal/dual search for these objects, followed by rigorous {\em certification} of their values. The search and certification are performed using AI tools, and in particular the rigorous certificates are very large (analytical reductions to thousands of numerical inequalities).
