Entanglement-Weighted Operator Geometry: Magnetic Monopoles and Winding problem

We present a comprehensive theory of magnetic monopoles within the framework of Entanglement-Weighted Operator Geometry (EWOG). Contrary to Dirac's point-like monopoles, EWOG predicts monopoles as topological solitons of the C-boson field $\mathcal{C}$, which encodes quantum coherence of spacetime. These monopoles emerge naturally from the weighted gauge Lagrangian and satisfy modified Maxwell equations. We derive the topological quantization condition connecting magnetic charge to the coherence charge $Q_C$, providing a solution to the long-standing monopole problem. The theory predicts specific signatures in the Cosmic Microwave Background (CMB) polarization patterns and offers connections to dark matter as clusters of these topological defects. We calculate the coherence coupling constant $\alpha$ from galactic rotation curves and demonstrate how weighted angular momentum conservation explains spiral arm preservation. The theory makes testable predictions for upcoming CMB experiments and gravitational wave observatories.