The electron and proton cores in the Planck vacuum (PV) theory are reccognizable elementary particles that obey the manisestly covariant Dirac equation and that are coupled to the PV state. (This statement and similar statements to follow also apply to the electron-core and the proton-core antiparticles.) This paper derives the corresponding 2x1 spinor-wavefunction equations for these cores, leading to a 7-dimensional spacetime that consists of two 4-dimensional spacetimes, the result of a bifurcated vacuum state. Both the electron and proton cores contain structure, where the electron core structure is orders of magnitude smaller than the proton-core structure. The core structure is easily reccognized in the calculations, as is particle-antiparticle annihilation. The difference between the electron and proton cores and their electron and proton particles is that the latter contain radiative corrections.
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