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  1. The precise value of the mean neutron lifetime, tau_n, plays an important role in nuclear and particle physics and cosmology. It is used to predict the ratio of protons to helium atoms in the primordial universe and to search for physics beyond the Standard Model of particle physics. We eliminated loss mechanisms present in previous trap experiments by levitating polarized ultracold neutrons above the surface of an asymmetric storage trap using a repulsive magnetic field gradient so that the stored neutrons do not interact with material trap walls. As a result of this approach and the use of an in situ neutron detector, the lifetime reported here [877.7 +/- 0.7 (stat) +0.4/-0.2 (sys) seconds] does not require corrections larger than the quoted uncertainties.