Where is the anomaly of polarized deep-inelastic scattering?

We demonstrate that the anomalous gluon contribution to the polarized proton structure function ${\mathit{G}}_1$, while in principle present, cannot be of sufficient magnitude to resolve the present dichotomy between the predictions of perturbative QCD and the results of the European Muon Collaboration experiment. In particular, we clarify the argument that data on unpolarized sea distributions can be used to rule out any large singlet component of ${\mathit{G}}_1$. Although, a priori, such a contribution could indeed be significant, the general requirements of positivity and a consistent application of the light-cone operator-product expansion to the quark-parton model imply rather stringent bounds on its magnitude. We interpret this failure of perturbative QCD as clear evidence that it is not applicable to physical processes involving real hadronic states.