The hypothesis that significant deposits of water ice exist in cold traps near lunar poles includes a supposition that acquired water is concentrated in the traps by exospheric lateral transport. That supposition, and by inference the trapped water hypothesis, are proven to be false by the present analysis of data obtained in 2013-2014 by the neutral mass spectrometer on the Lunar Atmosphere and Dust Environment Explorer (LADEE) spacecraft. These data show no evidence of exospheric water. The upper limit for exospheric water at the lunar surface, $\sim3$ molecules cm$^{-3}$, is deficient by several orders of magnitude in accounting for the deposition of the chondritic influx of water in cold traps. The present hypothesis is that the precursor of clay formation, cation exchange involving water molecules and anorthite, is analogous to reversible chemi-sorption, and that adsorbed water on the lunar surface is rapidly removed from the moon by solar wind sputtering.