Tuning the RADIO to the Off-Shell 2D Fayet Hypermultiplet Problem

We show via use of the RADIO technique that an off-shell (4,0) version of the hypermultiplet, in the form first proposed by Fayet, exists and contains 28 - 28 component fields. The off-shell structure uncovered is found to include a chiral truncation of the ``generalized 2D, N = 4 tensor multiplet formalism'' proposed by Ketov. The (4,0) theory is extended to an off-shell 56 - 56 component field (4,4) theory with the addition of a minimal (4,0) minus spinor multiplet together with (4,0) auxiliary multiplets. We propose that our final result gives a solution to a twenty year-old 2D supersymmetry problem in the physics literature.