Hard Nonlogarithmic Corrections of Order $m\alpha^7$ to Hyperfine Splitting in Positronium

We consider hard three-loop nonlogarithmic corrections of order $m\alpha^7$ to hyperfine splitting in positronium. All these contributions are generated by the graphs with photon and/or electron loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams. The total result for all these diagrams is $\Delta E=-1.2917(1)m\alpha^7/\pi^3=-5.672$ kHz.