Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation

Unconditional global existence and scattering are established for the three-dimensional focusing energy-critical generalized Hartree equation with $0<α<3$, below the ground-state energy and kinetic thresholds. The initial data lie in $\dot H^1$, with no radial symmetry, finite-mass, or finite-variance assumption. Annular frequency estimates and Gaussian interaction estimates rule out a compact critical trajectory by first controlling its nonlinear forcing and then recovering its conserved mass.