Search Results Reveal Video Dominance and Missing Algebraic Values for Rogers-Ramanujan Continued Fraction — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are dominated by introductory videos on the Rogers-Ramanujan continued fraction (RRCF), with one anomalous particle-physics paper (BESIII) on kaon form factors that is mathematically unrelated to the RRCF but contains a ratio of form factors. No exact algebraic values of RRCF singular moduli were retrieved.
MATH: - The RRCF is defined as R(q) = q1/5/(1 + q/(1 + q2/(1 + ⋯))). - For singular moduli (e.g., q = e−π√n), R(q) takes values in the real subfield of the Hilbert class field of ℚ(√(−n)). For n=5, R(e−2π) = √((5−√5)/2) − (√5−1)/2 (a known exact value in ℚ(√5)). - The BESIII paper reports the ratio |FKS|/|FKL| (neutral-to-charged kaon form factors) at Q2 between 12 and 25 GeV², showing flavor-SU(3) breaking — but this is unrelated to RRCF.
CONNECTION: - The RRCF at \( q = e^{-2\pi}
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Algebraic Units and Quintic Symmetry in Rogers-Ramanujan Continued Fraction Values — E8 Intelligence Research
- Rogers–Ramanujan Continued Fraction as Algebraic Key to Quintic Solvability — E8 Intelligence Research
- The Golden Ratio Bridge: Rogers-Ramanujan Continued Fraction and Quintic Solvability — E8 Intelligence Research
- Rogers-Ramanujan Continued Fraction at q = e^{-2π/5} Solves the General Quintic — E8 Intelligence Research
- Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction
BibTeX
@misc{caldin2026search,
title = {{Search Results Reveal Video Dominance and Missing Algebraic Values for Rogers-Ramanujan Continued Fraction — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23409973},
url = {https://zenodo.org/records/23409973},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Search Results Reveal Video Dominance and Missing Algebraic Values for Rogers-Ramanujan Continued Fraction — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23409973
UR - https://zenodo.org/records/23409973
AB - FINDING: The search results are dominated by introductory videos on the Rogers-Ramanujan continued fraction (RRCF), with one anomalous particle-physics paper (BESIII) on kaon form factors that is mathematically unrelated to the RRCF but contains a ratio of form factors. No exact algebraic values of RRCF singular moduli were retrieved. MATH: - The RRCF is defined as R(q) = q^1/5/(1 + q/(1 + q^2/(1 + ⋯))). - For singular moduli (e.g., q = e^−π√n), R(q) takes values in the real subfield of the Hilbert class field of ℚ(√(−n)). For n=5, R(e^−2π) = √((5−√5)/2) − (√5−1)/2 (a known exact value in ℚ(√5)). - The BESIII paper reports the ratio |F_K_S|/|F_K_L| (neutral-to-charged kaon form factors) at Q^2 between 12 and 25 GeV², showing flavor-SU(3) breaking — but this is unrelated to RRCF. CONNECTION: - The RRCF at \( q = e^{-2\pi} Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -