Version 1. 4 adds an independent comparison with Xu, Ye, and You (Phys. Rev. A 112, 062232, 2025) via a unified Bell-operator-norm diagnostic (new Sec. VII. E) ; a condensed verification note on the five-dimensional representation under sector-phase modulation (Appendix C) ; first-priority and prior-art hedging in the abstract, introduction, and conclusion; a corrected companion-paper attribution of the |S| = 3. 406 value to the cross-bipartition construction; finite-size framing of the referenced Z2 mutual-information result; affiliation simplified to "Independent Research, Germany"; and new references. No primary numerical result is changed. Abstract: We report a complete sequence-by-sequence numerical landscape of Bell-inequality violation across Fibonacci anyon braiding words of length L = 3 to 12 in two complementary encodings of six anyons. Earlier work by Brennen et al. established the existence of Bell-test constructions for Fibonacci anyons, and Xu, Ye, and You have independently studied three-copy CHSH correlations with maximum |S| ~ 2. 633; the present contribution is the complete enumeration over all braid words of a given length class. In the two-generator d1b encoding (native four-dimensional fusion space) the optimal sequence at L = 12 reaches |S| = 2. 811 (99. 4% of the Tsirelson bound), with concurrence C = 0. 988; in the five-dimensional encoding, Tsirelson saturation occurs already at L = 8. Bell violation is generic: a single topological mechanism (the sigma₃ cross-bipartition generator) gates whether entanglement is accessible — blocking it collapses concurrence to zero exactly. Sequential braiding produces positive lag-1 autocorrelation, a falsifiable prediction absent in standard quantum mechanics with independent measurement settings.
Berkay Yüksel Sayim (2026) studied this question.