arXiv:2611.14658v1 Announce Type: new Abstract: We derive a microscopic relation between the many-body Chern number $C$ of the fermionic ground state and the braiding of fluxes in $\mathbb{Z}_{2}$ gauge theory coupled to matter: under a spectral gap condition, dressed flux loops obey $W_2W_1=e^{i\frac{\pi}{2}C}W_1W_2$ on the ground-state sector. We realize $C=1$ by gauging charge parity in a weakly interacting Qi-Wu-Zhang insulator. Reflection positivity and chessboard estimates show that flux defects are massive, which yields a gapped, topologically ordered phase with four locally indistinguishable ground states.
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