A complementary theory effort to project B01 will ensure the interpretability of the experimental program, addressing both electroweak and hadronic corrections. The ambitious precision goal on the weak charge of the proton makes effects from radiative corrections as well as from hadronic and nuclear structure non-negligible and requires the interplay of theory with the high-level analysis of the experimental data. The results will also be analyzed in a global context, where they are complementary to the physics program at the LHC, for example Drell-Yan processes and measurements of the W boson mass, significantly advancing our understanding of the Standard Model.