Overviews on Berry-Keating conjecture, Hilbert-P\'{o}lya conjecture and Riemann hypothesis

Newly motivated by the G-dynamics as a part of the quantum covariant Hamiltonian system (QCHS), we try to use it to untangle the complex affairs of the three closely related conjectures: Riemann hypothesis (RH), Berry-Keating conjecture (BKC) and Hilbert-P\'{o}lya conjecture (HPC). Truly, a suitable solution $\zeta \left( 1/2+\sqrt{-1}{{w}^{\left( q \right)}} \right)=0$ holds for RH, it means that such an unbounded self-adjoint operator indeed exists, and it's the G-dynamics $\hat{w}^{(cl)}$ as a strong candidate for such self-adjoint operator which described the geometric frequency, exactly.