Pedagogical Videos on Jones Polynomial Omit Golden Ratio Evaluations — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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: Vtrefoil(t) = −t−4 + t−3 + t−1. At t = e2π i/5 (5th root of unity), V = −e−8π i/5 + e−6π i/5 + e−2π i/5. Numerically: V ≈ 0.618 + 0.786i (checking: e−2π i/5 ≈ 0.309 − 0.951i, e−6π i/5 ≈ −0.809 + 0.588i, −e−8π i/5 ≈ 0.309 + 0.951i; sum real = 0.309 - 0.809 + 0.309 = -0.191? Let me recompute precisely: e−2π i/5 = cos(72°) − isin(72°) = 0.3090 − 0.9511i. e−6π i/5 = cos(216°) − isin(216°) = −0.8090 + 0.5878i. −e−8π i/5 = −cos(288°) + isin(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 = e2π 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
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BibTeX
@misc{caldin2026pedagogical,
title = {{Pedagogical Videos on Jones Polynomial Omit Golden Ratio Evaluations — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526149},
url = {https://zenodo.org/records/23526149},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pedagogical Videos on Jones Polynomial Omit Golden Ratio Evaluations — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526149
UR - https://zenodo.org/records/23526149
AB - 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_trefoil(t) = −t^−4 + t^−3 + t^−1. At t = e^2π i/5 (5th root of unity), V = −e^−8π i/5 + e^−6π i/5 + e^−2π i/5. Numerically: V ≈ 0.618 + 0.786i (checking: e^−2π i/5 ≈ 0.309 − 0.951i, e^−6π i/5 ≈ −0.809 + 0.588i, −e^−8π i/5 ≈ 0.309 + 0.951i; sum real = 0.309 - 0.809 + 0.309 = -0.191? Let me recompute precisely: e^−2π i/5 = cos(72°) − isin(72°) = 0.3090 − 0.9511i. e^−6π i/5 = cos(216°) − isin(216°) = −0.8090 + 0.5878i. −e^−8π i/5 = −cos(288°) + isin(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^2π 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
ER -