Ammann-Beenker Tiling Inflation and Its Unresolved Link to CHSH Bound — E8 Intelligence Research

FINDING: Ammann-Beenker tiling inflation factor (1+√2) and its structural relation to the CHSH/Tsirelson bound is not directly established in the provided sources; the search results are mostly tangential (videos, unrelated transistor/steel topics). The only substantive mathematical item is the arXiv paper on Ammann-Beenker tilings as digitizations of 2D planes in 4D Euclidean space. MATH: - Ammann-Beenker tiling: 8-fold rotational symmetry (dihedral group D₄), inflation factor λ = 1 + √2 ≈ 2.41421356. - This λ is the silver ratio (δ_S = 1 + √2), satisfying λ² = 2λ + 1, and λ − 1/λ = 2. - The tiling is a projection of a 4D hypercubic lattice (Z⁴) onto a 2D plane, with the acceptance window being a regular octagon. - No explicit equation linking λ to the Tsirelson bound (2√2 ≈ 2.828) appears in the provided text. The Tsirelson bound is the maximal quantum violation of CHSH: S ≤ 2√2. Note: 2√2 = √(2(1+√2) + 2) — but this is a numerical coincidence unless proven otherwise; no evi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com