Search Results Reveal Video Dominance and Missing Algebraic Values for Rogers-Ramanujan Continued Fraction — E8 Intelligence Research

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 \( R(q) = \frac{q^{1/5}}{1 + \frac{q}{1 + \frac{q^2}{1 + \cdots}}} \). - For singular moduli (e.g., \( q = e^{-\pi\sqrt{n}} \)), \( R(q) \) takes values in the real subfield of the Hilbert class field of \( \mathbb{Q}(\sqrt{-n}) \). For \( n=5 \), \( R(e^{-2\pi}) = \sqrt{\frac{5-\sqrt{5}}{2}} - \frac{\sqrt{5}-1}{2} \) (a known exact value in \( \mathbb{Q}(\sqrt{5}) \)). - 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