  The widely-separated, near-equal mass binaries hosted by the cold Classical
Kuiper Belt are delicately bound and subject to disruption by many perturbing
processes. We use analytical arguments and numerical simulations to determine
their collisional lifetimes given various impactor size distributions, and
include the effects of mass-loss and multiple impacts over the lifetime of each
system. These collisional lifetimes constrain the population of small (R > ~1
km) objects currently residing in the Kuiper Belt, and confirm that the size
distribution slope at small size cannot be excessively steep - likely q < ~3.5.
We track mutual semi-major axis, inclination, and eccentricity evolution
through our simulations, and show that it is unlikely that the wide binary
population represents an evolved tail of the primordially-tight binary
population. We find that if the wide binaries are a collisionally-eroded
population, their primordial mutual orbit planes must have preferred to lie in
the plane of the solar system. Finally, we find that current limits on the size
distribution at small radii remain high enough that the prospect of detecting
dust-producing collisions in real-time in the Kuiper Belt with future optical
surveys is feasible.
