The Topological Chain Hypothesis: Topological Non-Separability from Dimensional Emergence

ABSTRACT We propose a framework in which physical reality is fundamentally a two-dimensional topological surface M², and quantum correlations—observed in Bell-type experiments as CHSH values above the classical bound—arise from the non-factorizability of anyonic fusion spaces built on M² rather than from nonlocal causal correlations. The structural label is the topological triple λ = (n, g, φT): winding number, genus, and topological phase. We show (i) that the d1b Fibonacci fusion space does not admit a tensor-product decomposition into spatially separated Alice/Bob Hilbert spaces; (ii) that on the n=8 Fibonacci fusion space of dimension D=F₇=13, using a sequential measurement protocol whose second setting contains the cross-bipartition generator σ₄, CHSH values up to |S|=3. 406 are attained; and (iii) that λ carries independent operational signatures at the level of reduced channel dynamics and winding-number quantization. (A third claimed signature via surface topology is retracted in v1. 6 — see Changelog below. ) The framework yields a specific correction to the quantum prediction, CTCH (a, b) = −cos θ + ε·f (n, g, θ). The dimensional hierarchy 0D → 1D → 2D → 3Dₚrojected is derived from three premises: existence, finitude, distinguishability. TCH is categorically distinct from superdeterminism under the timeless TQFT ontology adopted throughout. VERSION 1. 6 CHANGELOG Round 1 — Retraction of Predictions 1 and 6 following empirical tests (22 April 2026): Prediction 1 (detection-order autocorrelation ACF (1) ∈ 0. 24, 0. 59 in randomized-setting Bell experiments) was tested by reanalysis of Hensen et al. 2015 (N=245, MDE ≈ 0. 18 below the predicted lower bound). Measured ACF (1) = −0. 017 ± 0. 062, p=0. 87. Null hypothesis not rejected. Prediction retracted. Prediction 6 (genus-dependent Bell-fraction plateau as topology-specific signature) was tested on Fibonacci braiding simulations across S², T², T², Σ₂, Σ₃. The Σ₂/Σ₃ plateau at 93. 75% ± 0. 52pp is exactly reproduced by a non-topological random-diagonal-phase control, and a Haar-random U (5) baseline yields 100% Bell-fraction. Topology-specific interpretation retracted. Coupled passages retracted: black-hole-handle enhancement bridge, ACF-as-Bohm-discriminator, "Autocorrelation as a theorem" paragraph, Abstract ACF-range sentence and Claim (iii) third signature (BH-α v2). Round 2 — Integration of Track-A (derivation check) and Track-B (structural audit) findings (25 April 2026): §III. C has been substantially sharpened without altering the numerical result |S|=3. 406: Observable-edge labels corrected to (x₃, x₍-₂=x₆) to match the calculation. For n=8 with total charge VAC, Bob's observable MB = parity (x₆) = −I identically on all 13 basis states. The CHSH functional reduces to a one-party quantity with algebraic maximum 4; |S|=3. 406 is approximately 85% of this maximum. Not a genuine Tsirelson violation in the EPR-bipartite sense. Haar-random U (13) probes without any braid structure yield |S| ∈ 3. 16, 3. 75 over 200 samples; the phenomenon is generic to non-factorized D=13 observables, not Fibonacci-MTC-exclusive. What remains specific is the analytical handle: only σ₄ fails to commute with MA. Mechanism paragraph corrected: σ₄ appears in three of the four settings (A, A', B'), not only B'. §VIII. A Limitations table extended with three entries (Haar-U (13) universality; Fourier R²=0. 38 at L=12; Z₂-MI universality baseline open). New scope-boundary paragraph identifies framing elements (TCH label, dimensional-emergence narrative, neutral-monistic positioning, Van-Raamsdonk references) as not entering the §III. C derivation; their status is deferred to Paper 3 (in preparation). §IV. A qualifier on Z₂-MI (no Haar-baseline yet). §IV. C context note on 91. 8% Bell-fraction. §VI. C genus component of harmonic overtones removed. §I. C positive autocorrelation qualified as fixed-setting. §VIII. C Prediction 3 flagged as structurally coupled to Prediction 1. §VIII. D Protocol-dependence retitled "interpretive, not evidential". §VIII. F Conclusion list-sentence: "quantitative support" replaced by "first numerical construction". NOT AFFECTED: mathematical core §III (d1b non-factorisation, D=13 CHSH calculation, bipartition control ‖B‖=2. 000 in 8000/8000), dimensional hierarchy §II, measurement barrier §VI (apart from §VI. C genus term), response to Conway-Kochen §VIII. B, Predictions 2, 2b, 2c, 4, 5, 7, 8. Retracted passages marked "Retracted in v1. 6" in place; original v1. 5 text preserved inline for transparency.