QED Within The Differentially Cohesive (∞, 1)-Topos

We demonstrate that the cohesive (∞,1)-topos framework provides a first-principles, ge- ometric foundation for quantum electrodynamics (QED). We establish that fundamental QED predictions, such as the anomalous magnetic moment of the electron and the Lamb shift, can be derived directly from the internal logic and geometric structures of a differ- entially cohesive topos. The core of our work is the construction of a Cohesive-Feynman Dictionary, a series of theorems that rigorously identify abstract cohesive operations, such as modal curvature and cohesive pushforwards, with the concrete elements of perturbative QFT, including loop integrands, propagators, and vertex rules. This dictionary is then used to provide a complete, geometric derivation of the one-loop correction to the electron ver- tex, correctly reproducing the α/2π result for the anomalous magnetic moment. This work establishes that fundamental particle physics phenomena emerge as necessary consequences of the interplay between topology, geometry, and logic inherent to the cohesive framework.