Fibonacci Search: Recurrence, Binet's Formula, and Golden Ratio — E8 Intelligence Research

FINDING: The search results are dominated by popular expositions of the Fibonacci sequence and golden ratio, with one outlier on hexaquark decay — no direct hits on Fibonacci anyons, Temperley-Lieb algebras, or loop values. The mathematical core is the classical Fibonacci recurrence and its closed-form via Binet's formula. | MATH: Fibonacci recurrence \(Fₙ₊₁=F_n+Fₙ₋₁\), Binet's formula \(F_n = {φ^n - (-φ)⁻ⁿ}{√5}\), golden ratio \(φ = {1+√5}{2} ≈ 1.6180339887\), its inverse \(φ⁻¹ = φ - 1 ≈ 0.6180339887\), and the continued fraction \(φ = [1;1,1,1,]\) (slowest-converging irrational, hence "most irrational"). The hexaquark paper (arXiv:2012.11449) uses SU(3) group theory, not Fibonacci structure. | CONNECTION: The golden ratio is directly linked to geometric harmony: \(φ = 2cos(36^∘) = 2cos(π/5)\), which is the ratio of diagonal to side in a regular pentagon — the pentagon's symmetry group Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com