Three-Loop Corrections to Lamb Shift in Positronium: Electron Factor and Polarization

Hard spin-independent three-loop radiative contributions to energy levels in positronium generated by the two-photon-exchange diagrams with one-loop radiative insertions in the fermion lines and exchanged photons are calculated. This is a next step in calculations of all corrections of order $m\alpha^7$ inspired by the new generation of precise $1S-2S$ and $2S-2P$ measurements in positronium.