  Under the hypothesis of no topological structure below a certain scale, we
prove that any U(1) lattice configuration corresponds to a classical U(1) gauge
field with zero local field strength; i.e. any local representative of the
pullback connection one-form is a pure gauge and the local curvature two-form
is thus identical zero. The topological information is completely carried by
the chart transitions. To each such U(1) lattice configuration we assign a
Chern number, which generally depends on the reconstruction of the bundle and
is only unique under certain restrictions.
