We review the state-of-the-art and address open questions relative to thetheory uncertainty of the $\gamma-Z$ box contribution to the $A_{PV}$measurement within the QWEAK experiment at Jefferson Lab. This white papersummarizes the contributions by participants and discussion sessions on thistopic within the MITP Workshop on Precision Electroweak Physics held in Mainz,Germany, September 23 - October 11, 2013\url{http://indico.cern.ch/conferenceDisplay.py?confId=248072
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