The paper discusses the consequences of anomalous Ward identities in the context of non-abelian gauge theories, specifically SU(3) x SU(3). The authors show that these anomalies must satisfy consistency or integrability relations, which are derived from the structure of the gauge group. For the SU(3) x SU(3) case, they verify that the anomalies given by Bardeen satisfy these consistency relations. They also provide an explicit solution to the anomalous Ward identities, which describes all anomalous contributions to low-energy theorems, including strong five pseudoscalar interactions, K44, and one- and two-photon interactions with three pseudoscalars. The paper highlights that the form of the minimal anomaly is determined by the structure of the gauge group, making it model-independent. The authors also point out that some expressions in the literature are incorrect due to not considering the non-abelian structure of the group. The effective action derived from the solution of the anomalous Ward identities can be used to describe the physical consequences of the anomalies, providing a strong argument for the relevance of perturbation theory anomalies to the physical world.The paper discusses the consequences of anomalous Ward identities in the context of non-abelian gauge theories, specifically SU(3) x SU(3). The authors show that these anomalies must satisfy consistency or integrability relations, which are derived from the structure of the gauge group. For the SU(3) x SU(3) case, they verify that the anomalies given by Bardeen satisfy these consistency relations. They also provide an explicit solution to the anomalous Ward identities, which describes all anomalous contributions to low-energy theorems, including strong five pseudoscalar interactions, K44, and one- and two-photon interactions with three pseudoscalars. The paper highlights that the form of the minimal anomaly is determined by the structure of the gauge group, making it model-independent. The authors also point out that some expressions in the literature are incorrect due to not considering the non-abelian structure of the group. The effective action derived from the solution of the anomalous Ward identities can be used to describe the physical consequences of the anomalies, providing a strong argument for the relevance of perturbation theory anomalies to the physical world.