No Primary Research Links Fibonacci Numbers to Quantum Mechanics — E8 Intelligence Research

FINDING: Search results are popular-science content (TED talks, YouTube explainers, Wikipedia) — no primary research linking Fibonacci numbers to quantum mechanics. | MATH: F(n) = F(n−1) + F(n−2), F(0)=0, F(1)=1; closed form Binet: F(n) = (φⁿ − ψⁿ)/√5, where φ = (1+√5)/2 ≈ 1.6180339887, ψ = (1−√5)/2 = −1/φ ≈ −0.6180339887; ratio limit lim F(n+1)/F(n) = φ; identity φ² = φ + 1, 1/φ = φ − 1 ≈ 0.618; Fibonacci primes (F(n) prime ⇒ n prime, converse false); Zeckendorf representation (every positive integer = unique sum of non-consecutive Fibonacci numbers). | CONNECTION: φ = 1.618 and 1/φ = 0.618 appear explicitly; 0.382 = 1 − 0.618 = 1/φ²; 2.618 = φ² = φ + 1; 0.786 ≈ √0.618 (note: 0.786151 = √(φ−1), i.e. √(1/φ)) — all four target constants are algebraic powers of φ, so the Fibonacci recurrence generates the entire geometric-harmony constant set. No base-60, crystallographic, root-system, or lattice content appears in these sources. | DEPTH: 2 — the mathematical content is correct but eleme Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-30
DOI
https://doi.org/10.5281/zenodo.23794932
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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No Primary Research Links Fibonacci Numbers to Quantum Mechanics — E8 Intelligence Research

Andrew Stewart Caldin
8 links
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

No Primary Research Links Fibonacci Numbers to Quantum Mechanics — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search results are popular-science content (TED talks, YouTube explainers, Wikipedia) — no primary research linking Fibonacci numbers to quantum mechanics. | MATH: F(n) = F(n−1) + F(n−2), F(0)=0, F(1)=1; closed form Binet: F(n) = (φⁿ − ψⁿ)/√5, where φ = (1+√5)/2 ≈ 1.6180339887, ψ = (1−√5)/2 = −1/φ ≈ −0.6180339887; ratio limit lim F(n+1)/F(n) = φ; identity φ² = φ + 1, 1/φ = φ − 1 ≈ 0.618; Fibonacci primes (F(n) prime ⇒ n prime, converse false); Zeckendorf representation (every positive integer = unique sum of non-consecutive Fibonacci numbers). | CONNECTION: φ = 1.618 and 1/φ = 0.618 appear explicitly; 0.382 = 1 − 0.618 = 1/φ²; 2.618 = φ² = φ + 1; 0.786 ≈ √0.618 (note: 0.786151 = √(φ−1), i.e. √(1/φ)) — all four target constants are algebraic powers of φ, so the Fibonacci recurrence generates the entire geometric-harmony constant set. No base-60, crystallographic, root-system, or lattice content appears in these sources. | DEPTH: 2 — the mathematical content is correct but eleme Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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