  Cosmological bounces occur in many gravity theories. We define singularity
scattering maps relating large scale geometries before and after the bounce
(assuming no BKL oscillations) and encoding microscopic details of the theory.
By classifying all suitably local maps we uncover three universal laws: scaling
of Kasner exponents, canonical transformation of matter, directional metric
scaling. These are indeed obeyed by Bianchi I bounces in string theory, loop
quantum cosmology and modified matter models; our classification then
determines how inhomogeneities and anisotropies traverse bounces, and precisely
extracts model-dependent degrees of freedom.
