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 \(F_{n+1}=F_n+F_{n-1}\), Binet's formula \(F_n = \frac{\varphi^n - (-\varphi)^{-n}}{\sqrt{5}}\), golden ratio \(\varphi = \frac{1+\sqrt{5}}{2} \approx 1.6180339887\), its inverse \(\varphi^{-1} = \varphi - 1 \approx 0.6180339887\), and the continued fraction \(\varphi = [1;1,1,1,\dots]\) (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: \(\varphi = 2\cos(36^\circ) = 2\cos(\pi/5)\), 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