Novel Fibonacci Tree Representation Enables Closed-Form Direct Nth-Term Computation — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: ArXiv paper presents novel closed-form Fibonacci representation via Fibonacci trees enabling direct nth-term computation without recursion | MATH: F_n via Fibonacci tree representation (alternative to Binet's formula F_n = (φ^n - (-φ)^{-n})/√5, φ = (1+√5)/2 ≈ 1.618034) | CONNECTION: φ = 1.618... (golden ratio); 1/φ = φ-1 = 0.618...; φ^2 = φ+1 = 2.618...; √φ ≈ 1.272; φ^{-1/2} ≈ 0.786 — all present in standard Fibonacci asymptotics | DEPTH: 6 FINDING: Keith Devlin (Stanford) distinguishes mathematical fact from fiction regarding φ and Fibonacci in nature | MATH: φ = (1+√5)/2; Fibonacci recurrence F_{n+1} = F_n + F_{n-1}; limiting ratio lim F_{n+1}/F_n = φ | CONNECTION: Debunks spurious claims 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: W7225564847