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We investigate the problem of completing partial matrices to rank-one matrices in thestandard simplex ∆mn−1. The motivation for studying this problem comes from statistics: Alack of eligible completion can provide a falsification test for partial observations to come fromthe independence model. For each pattern of specified entries, we give equations and inequalitieswhich are satisfied if and only if an eligible completion exists. We also describe the set of validcompletions, and we optimize over this set.