Modeling the assembly of Lennard-Jones particles on a sphere (arXiv:2603.12360), researchers use a greedy nonequilibrium protocol: each new particle attaches to the most energetically favorable position, the system relaxes, and then the next particle arrives. No global optimization. No equilibrium search. Just one particle at a time, choosing the locally best spot.
The through-claim: greedy assembly reproduces global optima it never searches for. The resulting structures include well-known icosahedral viral capsid geometries — the same symmetric shells that viruses use to package their genomes. These structures emerge from a purely sequential, myopic process. No particle “knows” the final structure. Each simply minimizes its own energy upon arrival.
The mechanism works because the sphere constrains the search space. On a flat plane, greedy sequential assembly would produce disordered packings. But curvature forces geometric frustration — not all local optima are compatible with the surface — and this frustration guides the growing shell toward high-symmetry solutions. The constraint (spherical geometry) compensates for the algorithm's ignorance (no global search).
Novel structures also appear: square-triangular surface patterns with octahedral and tetrahedral symmetries, matching synthetic nanocontainers and natural protein complexes. Some of these don't correspond to any known equilibrium minimum — they're products of the assembly pathway itself. The process discovers structures that optimization would miss because they're dynamically accessible but not thermodynamically deepest. The path through the energy landscape visits places the landscape's minima don't predict.