Fibonacci Divisors, Golden Oscillators, and the Missing Jones–Trefoil–SU(2)₃ Link — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search returned mostly pedagogical content on Fibonacci/golden ratio plus one substantive arXiv paper linking Fibonacci divisors to N=2 supersymmetric "golden oscillators" via quantum calculus — but **no source directly establishes the Jones polynomial ↔ trefoil ↔ golden ratio ↔ SU(2)₃ Fibonacci TQFT chain** you specified. The core physics claim is only partially supported by the retrieved evidence.
MATH (from retrieved sources, verified): - Binet formula: F_n = (φⁿ − ψⁿ)/√5, with φ = (1+√5)/2 ≈ 1.6180339887, ψ = −1/φ ≈ −0.6180339887 - Golden ratio identities: φ² = φ + 1; 1/φ = φ − 1 = 0.6180339887; φⁿ = F_n φ + F_{n−1} - Silver ratio: δ_S = 1 + √2 ≈ 2.41421356 (appears in the arXiv paper's two-base quantum calculus) - arXiv:2410.04169v2: two-base quantum calculus with bases {φ, δ_S}; Fibonacci divisor derivative; Binet formula for Fibonacci divisor number operator in Fock space; hierarchy of "golden oscillators" with energy spectrum; fermion–boson entanglement
MATH (sta
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026fibonacci,
title = {{Fibonacci Divisors, Golden Oscillators, and the Missing Jones–Trefoil–SU(2)₃ Link — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658676},
url = {https://zenodo.org/records/23658676},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fibonacci Divisors, Golden Oscillators, and the Missing Jones–Trefoil–SU(2)₃ Link — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658676
UR - https://zenodo.org/records/23658676
AB - FINDING: The search returned mostly pedagogical content on Fibonacci/golden ratio plus one substantive arXiv paper linking Fibonacci divisors to N=2 supersymmetric "golden oscillators" via quantum calculus — but **no source directly establishes the Jones polynomial ↔ trefoil ↔ golden ratio ↔ SU(2)₃ Fibonacci TQFT chain** you specified. The core physics claim is only partially supported by the retrieved evidence. MATH (from retrieved sources, verified): - Binet formula: F_n = (φⁿ − ψⁿ)/√5, with φ = (1+√5)/2 ≈ 1.6180339887, ψ = −1/φ ≈ −0.6180339887 - Golden ratio identities: φ² = φ + 1; 1/φ = φ − 1 = 0.6180339887; φⁿ = F_n φ + F_{n−1} - Silver ratio: δ_S = 1 + √2 ≈ 2.41421356 (appears in the arXiv paper's two-base quantum calculus) - arXiv:2410.04169v2: two-base quantum calculus with bases {φ, δ_S}; Fibonacci divisor derivative; Binet formula for Fibonacci divisor number operator in Fock space; hierarchy of "golden oscillators" with energy spectrum; fermion–boson entanglement MATH (sta Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -