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 $gamma Z$ interference structure functions $F_1^{gamma Z}$ and $F_2^{gamma Z}$ used in those calculations, which are also used for determination of the two-boson exchange box diagram ($Box_{gamma Z}$) contribution to parity-violating elastic scattering measurements. A positive parity-violating asymmetry for inclusive $pi^-$ 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 $pi^-$ production.
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