Martel–Merle nonexistence conjecture for outgoing multi-solitons

Let $\phi$ solve the three-dimensional energy-critical wave equation and satisfy the no-outgoing-radiation condition, and consider multi-solitons whose ground-state components are the solitons under discussion. A ground-state multi-soliton nonexistence conjecture. There exists no solution satisfying the no-outgoing-radiation condition with more than one ground-state soliton. This conjecture concerns the obstruction created by the weak $r^{-3}$ far-field decay of the ground state and asserts nonexistence in the multi-soliton setting, although the supplied text does not state a resolution.