Wide-angle exclusive Compton scattering and single-pion photoproduction from the proton have been investigated via measurement of the polarization transfer from a circularly polarized photon beam to the recoil proton. The wide-angle Compton scattering polarization transfer was analyzed at an incident photon energy of 3.7~GeV at a proton scattering angle of cma$= 70^circ$. The longitudinal transfer KLL, measured to be $0.645 pm 0.059 pm 0.048$, where the first error is statistical and the second is systematic, has the same sign as predicted for the reaction mechanism in which the photon interacts with a single quark carrying the spin of the proton. However, the observed value is $sim$3~times larger than predicted by the generalized-parton-distribution-based calculations, which indicates a significant unknown contribution to the scattering amplitude.
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