Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the $L^2$-critical level

In this paper, we study the focusing mass-critical Hartree equation \[ iu_t+Δu=-\bigl(|x|^{-2}*|u|^2\bigr)u \] at the ground-state mass $M(Q)$. We prove that, up to the symmetries of the equation, every global minimal-mass non-scattering solution is a solitary wave, while every finite-time minimal-m