This paper describes the unfolding of the solar modulated galactic cosmic ray H and He nuclei spectra beyond ~105 AU in the heliosheath. Between 2008.0 and 2012.3 when Voyager 1 went from about 105 to 120.5 AU the spectral intensities of these two components between about 30 and 500 MeV/nuc unfolded (increased) in a manner consistent with an average modulation potential decrease ~5 MV per AU as described by a Parker like cosmic ray transport in the heliosphere where the overall modulation is described by a modulation potential in MV. Between 120.5 and 121.7 AU, however, as a result of two sudden intensity increases starting on May 8th and August 25th, 2012, this modulation potential decreased by ~80 MV and spectra resembling possible local interstellar spectra for H and He were revealed. Considering these spectra to be the local interstellar spectra would imply that almost 1/3 of the total modulation potential of about 270 MV required to explain the spectra of these components observed at the Earth must occur in just a 1 AU radial interval in the outer heliosheath. As a result about ~80% of the total modulation potential observed at the Earth at this time occurs in the heliosheath itself. The remaining 20% of the total modulation occurs inside the heliospheric termination shock. The details of these intensity changes and their description by a simple modulation model are discussed.
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