  Taking into account the global one-dimensionality conjecture recently
proposed by the author, the Cauchy-like analytical wave functional of the
Wheeler-DeWitt theory is derived. The crucial point of the integration strategy
is canceling of the singular behavior of the effective potential, which is
performed through the suitable change of variables introducing the invariant
global dimension. In addition, the conjecture is extended onto the wave
functionals dependent on both Matter felids as well as the invariant global
dimension. Through application of the reduction within the quantum gravity
model, the appropriate Dirac equation is obtained and than solved. The case of
superposition is also briey discussed.

General Relativity and Quantum Cosmology