Generic CHSH Violation in Fibonacci Anyon Braiding: A Landscape Analysis

We report the first, to our knowledge, complete sequence-by-sequence numerical landscape of CHSH-inequality violation across all Fibonacci anyon braiding words of length L = 3-12 in two complementary encodings of six anyons. In the two-generator d_1b encoding (native four-dimensional fusion space), the optimal sequence at L = 12 reaches |S| = 2.811 (99.4% of the Tsirelson bound 2√2) with concurrence C = 0.988. Throughout, "CHSH violation" denotes a CHSH value exceeding 2 on the Fibonacci fusion space, which does not factorize into spatially separated Alice/Bob subsystems; the reported values are signatures of topological nonseparability and single-algebra contextuality, not Bell violations in the Einstein-Podolsky-Rosen sense. In the three-generator encoding under four-dimensional computational-subspace projection, the enumeration maximum approaches the Tsirelson bound to within 0.16% already at L = 8. CHSH violation is generic: 64.6% of sequences violate the CHSH inequality at L = 9 under native five-dimensional measurement, rising to 91.8% under computational-subspace projection. A single topological mechanism controls this landscape: blocking the cross-bipartition generator σ3 collapses concurrence to C = 0 exactly for all sequences and all sector phases — topology acts as a gatekeeper for entanglement. Sequential braiding on a shared fusion space produces positive lag-1 autocorrelation ACF(1) = +0.34 at 10.85σ significance, a falsifiable state-continuity signature not predicted by standard quantum mechanics under independent measurement settings. Together with a companion mutual-information analysis of topological sectors and CHSH values, these results indicate that the available topological operations gate whether CHSH correlations are accessible on the fusion space. Version notes (v1.5, following a comprehensive internal review of the full series): • Table III (three-generator landscape) is corrected throughout. At L = 8, the previously reported |S| = 2.828, C = 1.000 (exact Tsirelson saturation) is corrected to |S| = 2.824, C = 0.997 (99.84% of the Tsirelson bound), matching the paper's own exhaustive 3^8-sequence search; all dependent statements are revised from "reaches/saturates Tsirelson" to "approaches the Tsirelson bound (within 0.16%)". Rows L = 3-7 are re-anchored to the canonical exhaustive-enumeration maxima, correcting the values reported in v1.0-v1.4 (2.815/2.822/2.825 → 2.722/2.791 with recomputed concurrences and percentages); per-L sequence entries are replaced by "(enumeration max)". • The computational-subspace fidelity N² (Table IV) is corrected: the normalization reported in v1.0-v1.4 omitted the factor 1/2 required by the orthonormal logical-basis projector; the corrected metric was verified via two independent computational routes. • The L = 3 CHSH-violation fraction is corrected from 48% to 44%. The thermal-poisoning statement is corrected: the rate is exponentially suppressed by the topological gap, not enhanced. A mis-stated evaluation count (800) is corrected to 200. The dominant-Fourier-harmonic identification is qualified as fit-method-dependent. A methods sentence describing the σ3 → identity numerical check is corrected. • The nonseparability/contextuality discussion is restructured from a footnote into a body subsection, and Appendix C is extended with the sector-phase-deformation analysis (generic δ ≠ 0 breaks the Yang-Baxter/hexagon consistency; only δ = 0 realizes the standard Fibonacci modular tensor category). • A footnote clarifies the generator-index convention relative to the companion cross-bipartition construction (the index shift is purely notational). The companion-work title is updated to match the companion paper's final title, and series-wide notation ("non-Abelian") is unified. • Correction: a corrupted footnote macro is repaired (the sigma-index-convention note now renders correctly); the topological-switch statement is scoped to the three-generator encoding; the sequential-braiding CHSH value is identified as the native five-dimensional (Protocol B) evaluation. • A lag-1 autocorrelation null control is added, computed on the openly available Hensen et al. (2015) loophole-free Bell dataset (4TU data DOI 10.4121/uuid:6e19e9b2-4a2d-40b5-8dd3-a660bf3c0a31, N = 245 valid trials); it is consistent with zero, as expected for independently re-prepared Bell trials. A six-term Fourier fit of S(δ) yields R² = 0.997 at L = 3, decreasing to R² = 0.38 at L = 12. The dephasing statement is corrected to match its own formula: pure dephasing bounds |S| from below by the classical value 2, attained only in the fully-dephased limit v → 0. The Pan (2008) citation is moved to the clause it supports (the neighboring fillings observed in the first excited Landau level). • The data and code availability statement is rewritten: all validation scripts and JSON outputs behind the published tables are now deposited (including the full ACF pipeline with the public Hensen et al. 2015 dataset), and the phrase "available upon request" is removed series-wide. Correction: the L = 6 row of Table I is re-anchored to the deposited sector-phase grid (2.398/0.662/84.8, correcting 2.394/0.658/84.7). An AI-use disclosure is added at the end of the paper. The canonical landscape-validation script and data (carried by the v1.4 record) are restored to the package, and the figure data files are added, so that every figure regenerates from the package alone; internal build annotations were removed from the LaTeX source (no printed content changed). • Corrections (pre-publication verification pass): the L = 4 and L = 7 rows of Table I are re-anchored to the deposited 50-point sector-phase grid (2.225/0.488/78.7 and 2.536/0.780/89.7, correcting 2.224/0.486/78.6 and 2.535/0.779/89.6 from the original coarser 25-point grid, the same correction class as the L = 6 row), and the enumeration sentence now names the deposited grid. The Pillar-2 null-test and initialization-robustness ACF values are re-anchored with a documented seed and a deposited script (d8_acf_null_robustness.py): ACF(1) = +0.001/+0.010 (previously -0.007/-0.019, both consistent with zero), robustness +0.318/+0.326 (previously +0.244/+0.296, unchanged conclusion), and the cross-setup range is restated as [0.31, 0.37] over the four deposited setups (previously [0.24, 0.50], whose upper end had no deposited generator). The top curve of Fig. 1(a) is regenerated from the deposited sweep data (previously plotted from values without a deposited source; the qualitative picture is unchanged). Two evaluation counts in the σ3-blocking section are corrected to match the deposited data (150 and 250, previously 200 in both places). One table entry (+12.4) is corrected to +12.3. The README inventory now lists the figures folder and the new script. • Release date set (2026-07-23). An author's note on the version history of this record is included as a separate file (author_note_version_history.pdf). About this series: This record is part of a series of related works from my independent research on Fibonacci anyons, with Ising anyons as their natural counterpart. I started in April 2026, and it has been a long and insightful journey in which I learned a lot; the work uses different methods and stays within verifiable, nonspeculative physics. The common thread of the series is a split: Ising anyons are limited to Clifford operations, while Fibonacci anyons are computationally universal, and across the series I map what standard witnesses of nonclassicality can and cannot certify on such systems. I consider Fibonacci anyons a serious candidate for topological quantum computing, given their universality and their topological protection against local noise. A hybrid approach with Ising is conceivable, but problems such as instability and certification would have to be solved first, and each needs research of its own. This paper asks whether CHSH violation in Fibonacci anyon braiding is typical rather than exceptional and maps the braid landscape systematically, where the violation turns out to be generic and close to the quantum bound, and it adds a predicted autocorrelation for sequential braiding in the shared fusion space together with a robustness analysis for real platforms; within the series it turns a single finding into a landscape and a testable signal. Use of AI tools: In the research, processing, and writing of this paper and its results I worked together with generative AI tools, in practice a system of multiple coordinated AI instances that I set up and orchestrate (large language models, mainly Claude, by Anthropic, inside Claude Code). At their current context sizes I found it far more effective to work with several specialized instances, each with its own role and its own harness of rules and parameters that I designed and refined through feedback, than to load a single instance with all of the material; for my workflow that would have been inefficient, though this depends on the individual implementation. I lead this collaboration: I choose the research directions, set the goals, and make the final decisions in open exchange with the AI, learning actively as the work proceeds. The AI carries out the drafting, including the mathematical and technical parts, the numerical computation, and the literature search, under my direction. The AI works autonomously only task by task, within the structure I develop through feedback: it completes a task, and at open questions that need me it stops until the point is settled before the next step. Along the way I witness and take many of the decisions that shape the path, and it is common for me to spot things that need improvement. The work spans many separate runs, and a single simulation or build task alone can take up to an hour, so it could not happen all together in one autonomous run; and had I let the AI do all of it together alone, even if it is possible, it would no longer be my work