{"id":"doi:10.5281/zenodo.18737070","kind":"article","title":"HopfionSeries Paper VIII - Geometry-Dependent Bell Violations From The Density-Feedback Hopfion","authors":["Frederick Manfredi"],"author_count":1,"year":2026,"published":"2026-02-22","venue":"Zenodo (CERN European Organization for Nuclear Research)","cited_by":5,"doi":"10.5281/zenodo.18737070","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.5281/zenodo.18737070","archive_url":"https://space-kitty.com/papers/doi:10.5281/zenodo.18737070","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W7131098971","pdf_url":null,"abstract":"We extend the density-feedback Faddeev–Niemi Hopfion framework of Papers I–VII to quantum Bell correlations. The suppression law S(θ) = sin4θ/φ6, derived from the Hopf map Jacobian in Paper I, together with measurement-induced density feedback 1/(1 + β(ρ + δρ)), generates a local deterministic model that reproduces quantum Bell correlations. The model avoids Bell’s theorem because the hidden variable is not a classical probability distribution over independent local properties but a single shared geometric flux line, a deterministic field structure whose angular correlations emerge from the suppression law. Structurally this is the Aharonov–Bohm situation: a single global, source-fixed connection fixes the correlation through its holonomy, with no local field or signal passing between the sites. In planar laboratory geometries, the configuration of every existing loophole-free Bell test, the model achieves CHSH ≈ 2.6 for density feedback β ≈ 0.452 & β ∈ [0.1, 1.0], within 7–9% of Tsirelson’s quantum bound 2√2 ≈ 2.828. The framework-fixed coupling β* ≈ 0.452 (determined from first principles by the Bogomolny structure of Papers I–VII) gives CHSHrescaled = 2.611, sitting smoothly within the scan range and confirming the result is not fine-tuned. The scaling 2.57–2.62 of the geometric rescale factor is a genuine geometric correction, not a fit parameter. Fully isotropic 3D sampling – where the hidden flux-line direction is distributed uniformly over the sphere rather than confined to the measurement plane – yields CHSH ≈ 1.7 even with standard detectors. Standard quantum mechanics predicts CHSH = 2.828 independent of geometry; this is the model’s primary falsifiable distinction. The model makes three testable predictions: (1) reduced Bell violations in multi-satellite quantum networks probing true 3D geometries; (2) continuous CHSH variation from ≈ 1.8 to ≈ 2.6 as detector back-action is varied from weak to projective measurements; and (3) φ-periodic corrections to the exact cos4 correlation form at the few-percent level. Monte Carlo simulations (N = 100,000) confirm robust violations in planar and biased geometries with smooth degradation toward the classical regime. Python simulation code is provided for independent verification.","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Quantum Mechanics and Applications"],"details":null,"provenance":"openalex","attribution":"Abstract of \"HopfionSeries Paper VIII - Geometry-Dependent Bell Violations From The Density-Feedback Hopfion\" by Frederick Manfredi, https://doi.org/10.5281/zenodo.18737070, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.","topics":[{"slug":"quantum-foundations","name":"Quantum Foundations","domain_slug":"physics"}],"cited_in_dossiers":[]}