Pedagogical Videos on Jones Polynomial Omit Golden Ratio Evaluations — E8 Intelligence Research

FINDING: The search returns only pedagogical videos on the Jones polynomial and trefoil knot, with no explicit mention of golden ratio evaluations or q-root-of-unity specializations. | MATH: Jones polynomial for trefoil: \( V_{\text{trefoil}}(t) = -t^{-4} + t^{-3} + t^{-1} \). At \( t = e^{2\pi i/5} \) (5th root of unity), \( V = -e^{-8\pi i/5} + e^{-6\pi i/5} + e^{-2\pi i/5} \). Numerically: \( V \approx 0.618 + 0.786i \) (checking: \( e^{-2\pi i/5} \approx 0.309 - 0.951i \), \( e^{-6\pi i/5} \approx -0.809 + 0.588i \), \( -e^{-8\pi i/5} \approx 0.309 + 0.951i \); sum real = 0.309 - 0.809 + 0.309 = -0.191? Let me recompute precisely: \( e^{-2\pi i/5} = \cos(72°) - i\sin(72°) = 0.3090 - 0.9511i \). \( e^{-6\pi i/5} = \cos(216°) - i\sin(216°) = -0.8090 + 0.5878i \). \( -e^{-8\pi i/5} = -\cos(288°) + i\sin(288°) = -0.3090 - 0.9511i \). Sum = (0.3090 - 0.8090 - 0.3090) + i(-0.9511 + 0.5878 - 0.9511) = -0.8090 - 1.3144i. Not golden. At \( t = e^{2\pi i/3} \): \( V = -e^{-8\pi i/3} + e^{-6\

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com