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

We present the complete result for the ${\cal O}(\alpha^7m_e)$ 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.