Non-existence of rest-frame spin-eigenstate spinors in their own electrodynamics

We assume a physical situation where gravity with torsion is neglected for an electrodynamically self-interacting spinor that will be taken in its rest-frame and spin-eigenstate: we demonstrate that under this circumstance no solution exists for the system of field equations. Despite such a situation might look artificial nevertheless it represents the instance that is commonly taken as the basis for all computations of quantum electrodynamics.