  In a previous paper, two of the authors presented a "regulated" picture of
eternal inflation. This picture both suggested and drew support from a
conjectured discontinuity in the amplitude for tunneling from positive to
negative vacuum energy, as the positive vacuum energy was sent to zero;
analytic and numerical arguments supporting this conjecture were given. Here we
show that this conjecture is false, but in an interesting way. There are no
cases where tunneling amplitudes are discontinuous at vanishing cosmological
constant; rather, the space of potentials separates into two regions. In one
region decay is strongly suppressed, and the proposed picture of eternal
inflation remains viable; sending the (false) vacuum energy to zero in this
region results in an absolutely stable asymptotically flat space. In the other
region, we argue that the space-time at vanishing cosmological constant is
unstable, but not asymptotically Minkowski. The consequences of our results for
theories of supersymmetry breaking are unchanged.
