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Abstract We derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski’s virial theorem bound to finite energies and gives the first non-trivial bound on ⟨Tr X 2⟩. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. Our best lower bounds are already a factor of ∼ 2 from existing Monte Carlo results.