  We investigate the tachyon profile of a time-symmetric rolling tachyon
solution to open string field theory. We algebraically construct the solution
of [arXiv:0707.4472] at 6th order in the marginal parameter, and numerically
evaluate the corresponding tachyon profile as well as the action and several
correlation functions containing the equation of motion. We find that the
marginal operator's singular self-OPE is properly regularized and all
quantities we examine are finite. In contrast to the widely studied
time-asymmetric case, the solution depends nontrivially on the strength of the
deformation parameter. For example, we find that the number and period of
oscillations of the tachyon field changes as the strength of the marginal
deformation is increased. We use the recent renormalization scheme of
[arXiv:1412.3466], which contains two free parameters. At finite deformation
parameter the tachyon profile depends on these parameters, while when the
deformation parameter is small, the solution becomes insensitive to them and
behaves like previously studied time-asymmetric rolling tachyon solutions. We
also show that convergence of perturbation series is not as straightforward as
in the time-asymmetric case with regular OPE, and find evidence that it may
depend on the renormalization constants.
