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Novel experimental techniques are required to make the next big leap in neutron electric dipole moment experimental sensitivity, both in terms of statistics and systematic error control. The nEDM experiment at the Spallation Neutron Source (nEDM@SNS) will implement the scheme of Golub & Lamoreaux [Phys. Rep., 237, 1 (1994)]. The unique properties of combining polarized ultracold neutrons, polarized 3 He, and superfluid 4 He will be exploited to provide a sensitivity to ∼ 10 −28 e · cm. Our cryogenic apparatus will deploy two small (3 L) measurement cells with a high density of ultracold neutrons produced and spin analyzed inmore »