This paper develops an ontologically rich explanation of the inner mechanics of the annihilation process, starting from a non-local hidden-variable (NLHV) design. This explains the process in terms of the handedness of matter and antimatter, the interaction of the electron and antielectron as they approach, the collapse of their discrete force structures and their reformation into photon structures. The process is more one of remanufacture than destruction. The resulting Cordus theory successfully explains para- and ortho-positronium annihilation. It explains the different photons output, the relative difference in lifetimes, and why Bhabha scattering sometimes happens instead. The theory exposes a deeper common mechanism for annihilation, pair-creation, and bonding.