The global minimum of a cluster decides which structure a simulation predicts. We present anneal, a global optimizer of communicating chains. Each chain draws its move by Thompson sampling from a Normal-Gamma posterior on quench depth. A stalled chain completes the orbits of a symmetric core. A chain retires on a Good-Turing estimate of its unseen mass, a rule with a Lean derivation. The chains share minima through an annealed-flow bank, and a ledger charges each force call to the chain that spent it. On 64 shared starts of LJ$_{38}$ and LJ$_{75}$ the hop matches the hit rate of GMIN, 64 of 64, at a lower median cost a paired test does not separate. On the Cambridge Morse table it reaches 145 of 244 targets and GMIN 131.

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