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Self-assembled configurations are versatile for applications in which liquid-mediated phenomena are employed to ensure that static or mild physical interactions between assembling blocks take advantage of local energy minima. For granular materials, however, a particle’s momentum in air leads to random collisions and the formation of disordered phases, eventually producing jammed configurations when densely packed. Therefore, unlike fluidic self-assembly, the self-assembly of dry particles typically lacks programmability based on density and ordering symmetry and has thus been limited in applications. Here, we present the self-assembly of particles with momentum, yielding regular arrays with programmable density and symmetry. The key is to embed anti-repellent structures, i.e., traps, that can capture kinetic particles individually and then robustly hold them against collisions with other momentum granules during a dynamic assembly procedure. By using anti-repellent traps, physical interactions between neighbouring particles can be inhibited, resolving many phenomena related to the uncertainty of space-sharing events in granular packing. With our self-assembly strategy, highly dense yet unjammed configurations are demonstrated, which conserve the inherent randomness in the location information of each granule in the trap and are useful for robust multilevel authentication systems as unique applications.