Hyperfine splitting in positronium to $\mathcal{O}({\alpha }^7{m}_e)$: one-photon annihilation contribution

We present the complete result for the $\mathcal{O}({\alpha }^7{m}_e)$ one-photon annihilation contribution to the hyperfine splitting of the ground state energy levels in positronium. Numerically it increases the prediction of quantum electrodynamics by $217\pm 1$ kHz.