  Let $p$ be a prime. The goal of this paper is to prove the Smoothness Theorem
5.1, and to explain how it provides a new proof of the Norm Residue Isomorphism
Theorem. It states, in particular, that a $(1,\infty)$-cyclotomic pair is
$(n,1)$-cyclotomic for all $n \geq 1$, solving by the affirmative part of the
Smoothness Conjecture 14.25 of [DCF0], in depth $e=1$.
