Presentation-Holonomy in Quantum Field Theory: Local Anomalies as Curvature, Global Anomalies as Holonomy

We show that framing dependence in Chern–Simons theory, SL(2,Z) duality actions, holographic scheme dependence, and 2-group backgrounds all fit a single mathematical pattern.Amplitudes are sections of complex lines over a presentation groupoid, and anomalies are obstructions to strict functoriality. We state the Presentation-Holonomy Principle: given a presentationgroupoid and a projective functor into complex lines, local anomalies are curvature classes of aninduced connection while global anomalies are flat holonomies (torsion phases). We then providea one-page atlas mapping Papers I–IV (this series) into this framework and a short algorithm forcomputing curvature and holonomy invariants in new models.