No Primary Source Ties CHSH Detection Thresholds to Silver Ratio or Pell Numbers — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search results are metadata-level only (video titles/descriptions); no primary source in this set establishes a detection-efficiency threshold for Bell/CHSH tests tied to the silver ratio or Pell numbers. | MATH: CHSH inequality: |S| ≤ 2 (local hidden variable bound); Tsirelson bound |S| ≤ 2√2 ≈ 2.828 (quantum max). Silver ratio δ_S = 1 + √2 ≈ 2.4142. Pell numbers: P_n = 2P_{n-1} + P_{n-2}, P_0=0, P_1=1 → 0,1,2,5,12,29,70,... Pell–Lucas companion: Q_n = 2Q_{n-1}+Q_{n-2}, Q_0=Q_1=2 → 2,2,6,14,34,... Ratios P_n/P_{n-1} → 1+√2 = δ_S. | CONNECTION: δ_S = 1+√2 is the fundamental unit of ℤ[√2]; its continued fraction is [2;2,2,2,...] (pure periodic), the "most irrational after φ" in the noble-number hierarchy. Note 2√2 = 2(δ_S − 1) = 2δ_S − 2, so the Tsirelson bound is a direct affine image of the silver ratio: |S|_max = 2(δ_S − 1). This is the only rigorous geometric-harmony link the evidence supports. | DEPTH: 3 Precise breakdown of what the evidence does and does not support: 1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225199278