Name-to-rod map

At every cut a surviving carrier name $a$ has a prescribed spatial position $x(a)\in U$. Its rod coordinates are

The same declared frame $(e_0,e_1,e_2,e_3)$ interprets the numerical tensor components of $\delta (k)$.

In particular, the four momenta of a label are auxiliary components in a common local frame. They are not four quantum names and are not four globally propagating states on the cone.