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.

{"references": ["G. Wang. A study of generalized covariant Hamilton systems on generalized Poisson manifold [J].arXiv:1710.10597", "G. Wang. Analogy between geodesic equation and the GCHS on Riemannian manifolds [J].arXiv:2002.10825", "G. Wang. Generalized geometric commutator theory and quantum geometric bracket and its uses [J]. arXiv:2001.08566", "G. Wang. The G-dynamics of the QCPB theory [J].arXiv:2004.01001"]}

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