Scretching–Planck Density and Phase in Quantum Theory II

The Scretching–Planck (SP) density–phase action is locally equivalent to the Schrödinger equation wherever the density is positive. Reconstructing a global wavefunction also requires single-valuedness and compatibility with nodal and boundary conditions. Relativistic and gauge extensions require independently specified fields and dynamics. Varying the gauged matter action together with a separately chosen parity-even gauge kinetic term yields the classical Yang–Mills equations. On a finite spatial lattice, the spectral gap in the physical sector is given by the vacuum-weighted Poincaré constant with the Hamiltonian’s kinetic prefactor. Constructing the four-dimensional continuum theory and establishing a uniform positive gap in physical units remain open. For hydrogen, the reduced-mass Coulomb calculation gives a ground-state energy of −13.5982873 eV and a 1S–2P interval of 10.1987154 eV before additional recoil and level corrections.