  We show that the Huang-Ji-Yin (HJY) Gap Conjecture concerning CR mappings
between spheres follows from a conjecture regarding Sums of Squares (SOS) of
polynomials. The connection between the two problems is made by the CR Gauss
equation and the fact that the former conjecture follows from the latter
follows from a recent result, due to the author, on partial rigidity of CR
mappings of strictly pseudoconvex hypersurfaces into spheres.
