  In this contribution we sketch a branch-cut quantum formulation of the
Wheeler-DeWitt equation analytically continued to the complex plane. As a
starting point, we base our approach on the Ho\v{r}ava-Lifshitz formulation of
gravity, which employs higher spatial-derivative terms of the spacetime
curvature for renormalisation reasons. Following standard procedures, the
quantization of the Lagrangian density is achieved by raising the Hamiltonian,
the dynamical variable which represents the branch-cut complex scale factor and
the conjugate momentum to the category of operators. We arrive at an
Schr\"odinger-type equation with a non-linear potential. Solutions are then
obtained and discussed for different potential parameterizations. The results
reinforce the conception of a quantum leap between the contraction and
expansion phases of the branch-cut universe, in good agreement with the
Bekenstein criterion.
