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Parity-Violating Inelastic Electron-Proton Scattering at Low $Q^2$ Above the Resonance Region

We report the measurement of the parity-violating asymmetry for the inelastic scattering of electrons from the proton, at $Q^2 = 0.082$ GeV$^2$ and $ W = 2.23$ GeV, above the resonance region. The result $A_{\rm Inel} = - 13.5 \pm 2.0 ({\rm stat}) \pm 3.9 ({\rm syst})$~ppm agrees with theoretical calculations, and helps to validate the modeling of the $γZ$ interference structure functions $F_1^{γZ}$ and $F_2^{γZ}$ used in those calculations, which are also used for determination of the two-boson exchange box diagram ($\Box_{γZ}$) contribution to parity-violating elastic scattering measurements. A positive parity-violating asymmetry for inclusive $π^-$ production was observed, as well as positive beam-normal single-spin asymmetry for scattered electrons and a negative beam-normal single-spin asymmetry for inclusive $π^-$ production.