  We consider the totally asymmetric simple exclusion process with
\emph{soft-shock} initial particle density, which is a step function increasing
in the direction of flow and the step size chosen small to admit KPZ scaling.
The initial configuration is deterministic and the dynamics create a shock.
  We prove that the fluctuations of a particle at the macroscopic position of
the shock converge to the maximum of two independent GOE Tracy-Widom random
variables, which establishes a conjecture of Ferrari and Nejjar. Furthermore,
we show the joint fluctuations of particles near the shock are determined by
the maximum of two lines described in terms of these two random variables. The
microscopic position of the shock is then seen to be their difference.
  Our proofs rely on determinantal formulae and a novel factorization of the
associated kernels.
