  We provide an evolutionary formulation of a generic quantum cosmology. Our
starting point is the request that all quantities living on the slicing have to
be 3-tensors. This statement, when applied to the lapse function and the shift
vector, yields the no longer vanishing behavior of the super-Hamiltonian. Then,
we provide the formulation of an evolutionary quantum cosmology in
correspondence to a generic Universe asymptotically to the initial singularity.
