Search Results Largely Tangential to Query on j-Invariant and CM Points — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are largely tangential to the stated query (j-invariant, CM points, class field theory). The only mathematically substantive items are: (1) a geometric proof that the golden ratio is the diagonal of a unit regular pentagon, and (2) an arXiv paper on higher class field theory of arithmetic schemes (Wiesend-style) — neither directly addresses CM points or j-invariant singular moduli. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.6180339887; satisfies φ² = φ + 1, 1/φ = φ − 1 ≈ 0.6180339887. In a regular pentagon with side 1, diagonal d = φ (by Ptolemy's theorem on the cyclic quadrilateral formed by four vertices: d² = d + 1). The arXiv paper (0711.4485v3) concerns class field theory for arithmetic schemes, but no explicit equations, constants, or j-invariant relations are given in the abstract. | CONNECTION: The pentagon's diagonal ratio φ is directly tied to the dihedral symmetry D5 (order 10) — the crystallographic point group of a regular pentagon, which is non-crys
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026search,
title = {{Search Results Largely Tangential to Query on j-Invariant and CM Points — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23410037},
url = {https://zenodo.org/records/23410037},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Search Results Largely Tangential to Query on j-Invariant and CM Points — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23410037
UR - https://zenodo.org/records/23410037
AB - FINDING: The search results are largely tangential to the stated query (j-invariant, CM points, class field theory). The only mathematically substantive items are: (1) a geometric proof that the golden ratio is the diagonal of a unit regular pentagon, and (2) an arXiv paper on higher class field theory of arithmetic schemes (Wiesend-style) — neither directly addresses CM points or j-invariant singular moduli. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.6180339887; satisfies φ² = φ + 1, 1/φ = φ − 1 ≈ 0.6180339887. In a regular pentagon with side 1, diagonal d = φ (by Ptolemy's theorem on the cyclic quadrilateral formed by four vertices: d² = d + 1). The arXiv paper (0711.4485v3) concerns class field theory for arithmetic schemes, but no explicit equations, constants, or j-invariant relations are given in the abstract. | CONNECTION: The pentagon's diagonal ratio φ is directly tied to the dihedral symmetry D5 (order 10) — the crystallographic point group of a regular pentagon, which is non-crys Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -