  We present an exact solution of open bosonic string field theory which can be
used to describe any time-independent open string background. The solution
generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes
the existence of boundary condition changing operators with nonsingular OPEs
and vanishing conformal dimension. Our main observation is that boundary
condition changing operators of this kind can describe nearly any open string
background provided the background shift is accompanied by a timelike Wilson
line of sufficient strength. As an application we analyze the tachyon lump
describing the formation of a D$(p-1)$-brane in the string field theory of a
D$p$-brane, for generic compactification radius. This not only provides a proof
of Sen's second conjecture, but also gives explicit examples of higher energy
solutions, confirming analytically that string field theory can "reverse" the
direction of the worldsheet RG flow. We also find multiple D-brane solutions,
demonstrating that string field theory can add Chan-Paton factors and change
the rank of the gauge group. Finally, we show how the solution provides a
remarkably simple and nonperturbative proof of the background independence of
open bosonic string field theory.
