  A conjecture of Nazarov--Treil--Volberg on the two weight inequality for the
Hilbert transform is verified. Given two non-negative Borel measures u and w on
the real line, the Hilbert transform $H_u$ maps $L^2(u)$ to $L^2(w)$ if and
only if the pair of measures of satisfy a Poisson $A_2$ condition, and dual
collections of testing conditions, uniformly over all intervals. This
strengthens a prior characterization of Lacey-Sawyer-Shen-Uriate-Tuero
arxiv:1201.4319. The latter paper includes a `Global to Local' reduction. This
article solves the Local problem.
