Absence of Jung Constant Proofs in L^p Spaces; GCR Hypersurfaces in Minkowski Spaces — E8 Intelligence Research

FINDING: The search results are a scattered mix of standard L^p space lecture videos and unrelated golden ratio videos; no actual "Jung constant" or sharp constant proof for L^p spaces is present. The only mathematically substantive item is an arXiv paper on generalized constant ratio (GCR) hypersurfaces in Minkowski spaces. MATH: - L^p spaces: \(\|f\|_p = (\int |f|^p d\mu)^{1/p}\), Hölder: \(\|fg\|_1 \le \|f\|_p \|g\|_q\) for \(1/p+1/q=1\), Minkowski: \(\|f+g\|_p \le \|f\|_p + \|g\|_p\). - Golden ratio: \(\phi = (1+\sqrt{5})/2 = 1.618...\), with \(\phi^{-1} = 0.618...\), \(\phi^{-2} = 0.382...\). - GCR hypersurface condition: tangential part of position vector is a principal direction — implies specific curvature relations, but no explicit equation given in the abstract. CONNECTION: - No direct link between L^p sharp constants and golden ratio appears in these results. - The GCR hypersurface paper is in Minkowski (Lorentzian) geometry — its constant ratio condition may rel Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com