Disordered hyperuniformity implies a long-ranged direct correlation function (the Ornstein–Zernike equation). In an equilibrium many-particle system, this requires delicately designed effectively long-ranged interactions, which are not necessary for the dynamic self-assembly of non-equilibrium hyperuniform states. In 2019, Ni and co-workers theoretically predicted a non-equilibrium strongly hyperuniform fluid phase that exists in systems of circularly swimming active hard spheres, which was confirmed experimentally in 2022.