  We develop efficient algorithms for level-truncation computations in open
bosonic string field theory. We determine the classical action in the universal
subspace to level (18,54) and apply this knowledge to numerical evaluations of
the tachyon condensate string field. We obtain two main sets of results. First,
we directly compute the solutions up to level L=18 by extremizing the
level-truncated action. Second, we obtain predictions for the solutions for L >
18 from an extrapolation to higher levels of the functional form of the tachyon
effective action. We find that the energy of the stable vacuum overshoots -1
(in units of the brane tension) at L=14, reaches a minimum E_min = -1.00063 at
L ~ 28 and approaches with spectacular accuracy the predicted answer of -1 as L
-> infinity. Our data are entirely consistent with the recent perturbative
analysis of Taylor and strongly support the idea that level-truncation is a
convergent approximation scheme. We also check systematically that our
numerical solution, which obeys the Siegel gauge condition, actually satisfies
the full gauge-invariant equations of motion. Finally we investigate the
presence of analytic patterns in the coefficients of the tachyon string field,
which we are able to reliably estimate in the L -> infinity limit.
