Setting-Locality Violation and a Trans-Tsirelson CHSH Value on a Fibonacci Fusion Space

Version 1. 8 sharpens the title to name the setting-locality mechanism explicitly (the Tsirelson precondition that fails here) and adds one future-direction sentence in the Outlook; the content and all numerical results are unchanged from v1. 7. Version 1. 7 (carried forward): a focused, self-contained Letter reporting a sequential measurement protocol on the n=8 Fibonacci-anyon fusion space (D=F7=13) whose CHSH expectation attains |S|=3. 406, exceeding Tsirelson's bound. Two interpretive caveats are stated prominently: (i) this is a CHSH-form expression on a non-factorized fusion space, not a bipartite Bell violation in the EPR sense — Bob's observable is constant on the vacuum sector and the overshoot is driven by the cross-bipartition generator sigma₄ violating setting-locality (a controlled test without sigma₄ recovers ||B||=2. 000 exactly) ; (ii) |S|=3. 406 is not a supremum on D=13. The predictive framework and broader interpretive reading of earlier versions are deferred to separate forthcoming work and are not part of the claims here. Two corrections from earlier versions are stated for transparency: the dimension label (D=13, not "native 5D") and the mechanism framing (setting-locality, not an EPR Bell violation). Includes an independent comparison with Xu, Ye, and You and a unified Bell-operator-norm diagnostic. This preprint is part of a series on Bell and Leggett-Garg correlations in Fibonacci-anyon braiding (companion records: Paper 1a 10. 5281/zenodo. 19600752, Paper 1b 10. 5281/zenodo. 19601352, LGI-Letter 10. 5281/zenodo. 20372744). Further work, including a systematic study across the SU (2) ₖ anyon family, is planned as a follow-up.