  The p-adic AdS/CFT correspondence relates a CFT living on the p-adic numbers
to a system living on the Bruhat-Tits tree. Modifying our earlier proposal for
a tensor network realization of p-adic AdS/CFT, we prove that the path integral
of a p-adic CFT is equivalent to a tensor network on the Bruhat-Tits tree, in
the sense that the tensor network reproduces all correlation functions of the
p-adic CFT. Our rules give an explicit tensor network for any p-adic CFT (as
axiomatized by Melzer), and can be applied not only to the p-adic plane, but
also to compute any correlation functions on higher genus p-adic curves.
Finally, we apply them to define and study RG flows in p-adic CFTs,
establishing in particular that any IR fixed point is itself a p-adic CFT.
