Paper 6: Holonomy Without Curvature - A Flagship Demonstration in the Presentation-Scheme-Bundle Framework

We provide a definitive, checkable demonstration of a “flat-but-holonomic” anomaly invariantin the presentation/scheme-bundle framework: along an explicitly constructed loop of admissiblebackground data, the pulled-back local anomaly curvature vanishes, yet the amplitude lineacquires a nontrivial U(1) phase. We prove this phase is invariant under the full class ofadmissible local counterterms. The main text gives a quantized torsion 2-group flagship example(root-of-unity holonomy) with a fully explicit computation; a concise Appendix provides acontinuous large-gauge holographic example (AdS5) exhibiting the same mechanism.