Based on experimental evidence from scanning tunneling microscopy and spectroscopy, angle-resolved photoemission spectroscopy, and neutronscattering in high-temperature uperconductors,we present a unified theoretical framework that the confined electrons within polyhedral quantum wells as the Mott ground state and the symmetry-breaking of electron-proton pair as the superconducting mechanism. The new theory enables the analytical determination of fundamental properties in copper- andiron-based superconductors. These properties include the magic doping and checkerboard charge order, Fermi surface structure and its splitting, the symmetry and value of the superconducting energy gap, the superconductingtransition temperature, and the spin resonance peaks and their parity. The theoretical predictions of our model show strong agreement with experimental findings. Moreover, our research offers novel insights into the microscopic nature of magnetism, spin, holes, localized Cooper pair, magnetic monopoles, the Ginzburg-Landau order parameter, and the Meissner effect.