Topological Information in Bell Correlations: Mutual Information Between Topological Sectors and CHSH Values in 2D Lattice Models

Version 2.1 adds a finite-size scaling analysis of the Z2 sector–CHSH mutual information (new Sec. III.A): I(T;S) is measured at lattice sizes L = 8 to 64 with two independent Monte-Carlo engines and BIC model selection. The L = 16 signal is found to be a finite-size effect that decays toward zero with system size; the abstract wording is aligned with this finding. Table I (the Fibonacci-anyon CHSH landscape) is reproduced from the companion landscape paper via full Horodecki-bound enumeration. Affiliation simplified to "Independent Research, Germany"; bibliography updated with prior-art and related-work references; no primary numerical result is retracted. Abstract: We quantify the mutual information I(T;S) between topological sector labels T and CHSH values S in two-dimensional lattice models. In the Z2 lattice gauge theory on a 16x16 torus at inverse temperature beta = 2.0, we measure I = 0.015 +/- 0.011 bits, significant at >2 sigma in 9 of 10 independent Monte-Carlo runs (corroborated by gauge-invariant plaquette-strip observables, I = 0.035 +/- 0.016 bits). A finite-size scaling analysis indicates this sector–CHSH mutual information decays toward zero with system size. In the quantum toric code, abelian Z2 anyons produce no local Bell correlations. Three classical mechanisms for Bell violation are tested and ruled out, confirming Fine's theorem empirically. Fibonacci-anyon braiding in the fusion space produces, in simulation, Bell violation with |S| = 2.811 (99.4% of the Tsirelson bound), strongly sector-dependent: topology does not create or destroy entanglement but determines the measurement basis required to observe it.