  Three-velocity ballistic annihilation is an interacting system in which
stationary, left-, and right-moving particles are placed at random throughout
the real line and mutually annihilate upon colliding. We introduce a coalescing
variant in which collisions may generate new particles. For a symmetric
three-parameter family of such systems, we compute the survival probability of
stationary particles at a given initial density. This allows us to describe a
phase-transition for stationary particle survival.
