No Literature Linking Octagonal Ammann–Beenker Quasicrystals to Bell Inequality Tests — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search returned no source connecting octagonal quasicrystals (Ammann–Beenker) to Bell inequality tests; the two topics appear in disjoint literature sets. | MATH: Ammann–Beenker tiling = 8-fold (octagonal) quasiperiodic tiling, vertex set from Z-module generated by {1, e^{iπ/4}}; inflation ratio = silver ratio δ_S = 1+√2 ≈ 2.41421; substitution matrix eigenvalue δ_S; diffraction pattern has 8-fold symmetry (D₈), not crystallographic (C₈ forbidden by crystallographic restriction theorem). Bell: CHSH bound S ≤ 2 (local hidden variables) vs S ≤ 2√2 ≈ 2.828 (Tsirelson, quantum). | CONNECTION: Silver ratio 1+√2 is the octagonal analogue of the golden ratio φ=1.618 (pentagonal/icosahedral). Both are Pisot–Vijayaraghavan units: φ²=φ+1, δ_S²=2δ_S+1. Neither 0.382, 0.618, 0.786, 1.618, 2.618 nor base-60 appears in the retrieved sources. | DEPTH: 2 FINDING: No evidence in the retrieved material supports a mathematical link between quasicrystal tiling geometry and Bell-inequality violat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225271282
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