AI 中文总结
研究库珀伯格六圆柱猜想，通过计算机辅助将其简化为有限案例分析，对2,954,984种情况验证有理系数多项式不等式，证明最多六个两两不重叠的无限单位圆柱可同时与单位球相切。
AI 中文摘要
我们证明了最多六个两两不重叠的无限单位圆柱可以同时与一个单位球相切。六个是可以达到的，所以库珀伯格问题的答案恰好是六个。证明是计算机辅助的，即该陈述被简化为对2,954,984种情况的有限案例分析，在每种情况下，一个程序验证具有有理系数的显式多项式之间的三个不等式之一在一个盒子中始终成立。每个案例都是基本的算术检查，并且案例的完整列表随论文一起提供。
英文摘要
We prove that at most six pairwise non-overlapping infinite unit cylinders can simultaneously touch a unit ball. Six is achievable, so the answer to Kuperberg's question is exactly six. The proof is computer-assisted in the following sense: the statement is reduced to a finite case analysis with 2,954,984 cases, and in each case a program verifies that one of three inequalities between explicit polynomials with rational coefficients holds throughout a box. Each case is an elementary arithmetic check, and the complete list of cases is provided with the paper.
