论文标题
在“ $ d = 2 $和$ d = 3 $的随机关闭包装的显式分析解决方案上，请回复W. T. Kranz”
Reply to W. T. Kranz on "Explicit analytical solution for random close packing in $d=2$ and $d=3$"
论文作者
论文摘要
W. T. Kranz的最新评论被证明受到严重的数学错误的困扰，这使得其结论无效。
A recent Comment by W. T. Kranz is shown to be plagued by a serious mathematical error which makes its conclusions invalid.
