The QCPB theory for Riemann zeta function and quantum gravity

Enlightened by the QCPB for the definition of the QCHS which compatibly induces the G-dynamics as a brand-new dynamics for describing the quantum mechanics, it nicely provides such a new physical tool for us better understanding how quantum gravity would be.  Using this new tool,  we affirmatively prove the Hilbert-P\'{o}lya conjecture in G-dynamics, and then we confirm the exact form of the non-trivial zeros $\rho =1/2+\sqrt{-1}{{w}^{\left( q \right)}}$ validly for Riemann hypothesis that is accordingly proven $\zeta \left(\rho\right)=0$ to be interpreted as a quantum stable state of equilibrium for discrete variable ${w}^{\left( q \right)}$.

Since the $n$-manifolds admits an Einstein metric,  by considering  two-manifolds with Einstein metric, it is then geometrically proved that the non-trivial zeros of Riemann zeta function actually exist as a quantified set for quantum gravity (QG) such that identical equation ${{G}_{ij}}=\zeta \left(\rho\right)=0$ always holds on the two-manifolds by applying the quantum covariant Hamiltonian system defined by QCPB theory based on the Schr\"{o}dinger equation, where the geometric frequency ${w}^{\left( q \right)}= R$ that relates to the discrete energy spectrum of quantum gravity, and the scalar curvature $R$ in the vacuum field equation forms a discrete set.