Covariance, relativity, and the proper mass of the universe in the no-boundary wave function

A discrete class of privileged reference frames in a closed universe with identical equations of motion for physical degrees of freedom was found. A representation of the quantum state of the universe in a privileged reference frame was obtained as a Euclidean functional integral with no-boundary conditions. The boundary condition at the Pole, in addition to the smoothness conditions, is the infinite asymptotic behavior of the Hubble parameter. This makes it possible to regularize the functional integral by changing the sign of the expansion energy of the universe. The proposed construction also allows for the addition of a non-zero proper mass of the universe.