Joints theorem
= Joints theorem
{title2=$|J|\lesssim_n L^{n/(n-1)}$}
= Joints conjecture
{synonym}
The number of <joints of a line collection> formed by $L$ distinct real affine lines in $\mathbb R^n$ is at most $C_n L^{n/(n-1)}$. The <pruning and minimal-degree polynomial argument> proves this bound. The exponent is sharp: the coordinate-line grid has $m^n$ <joints of a line collection> and $n m^{n-1}$ lines. In three dimensions the bound is $C L^{3/2}$.