  The argument for the sufficiency of these conditions is also straightforward. If λ-distribution held, it would be possible in theory to arrange ensembles of particle pairs in which controllable probabilistic dependence would not be washed out, and accordingly the statistics of distant outcomes would depend on the nearby controllable factor. (For a proof that these conditions are sufficient for superluminal signaling in certain deterministic hidden variables theories, see Valentini 2002.)