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In presence of ABJ anomalies the familiar chiral symmetry of massless QED in 3+1 spacetime dimensions develops an interesting example of higher structure. In this talk we will explain that the higher structure of chiral symmetry is "physical", meaning that (1) it can be detected in specific correlators, and that (2) it implies selection rules and Ward-Takahashi identities for massless QED on curved spacetimes.