Defect McKay-Thompson Series Preserve Genus-Zero Hauptmodul Structure — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are dominated by noise (perovskite battery talks, Thompson sampling ML, metabolomics chromatography, and a Conway interview), but one substantive item emerges: a 2024 arXiv paper (2408.16263v2) extending McKay-Thompson series to "defect" versions, preserving genus-zero Hauptmodul structure. | MATH: Classical McKay-Thompson series Tg(q) = q−1 + O(q) for g ∈ 𝕄 (Monster group) are Hauptmoduln for genus-zero subgroups of SL(2,ℝ). The new work (Lin–Shao 2021, extended in 2408.16263) constructs twined partition functions Zg(τ) for defect lines in the Monster CFT, requiring modular invariance groups that are still genus-zero. Key constants: the Monster order |𝕄| = 808017424794512875886459904961710757005754368000000000 ≈ 8.08 × 1053; the minimal faithful representation dimension 196883; the identity element gives T1(q) = j(q) − 744 where \( j(q) = q^{-1} + 196884q + 21493760q^2 +
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026defect,
title = {{Defect McKay-Thompson Series Preserve Genus-Zero Hauptmodul Structure — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526439},
url = {https://zenodo.org/records/23526439},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Defect McKay-Thompson Series Preserve Genus-Zero Hauptmodul Structure — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526439
UR - https://zenodo.org/records/23526439
AB - FINDING: The search results are dominated by noise (perovskite battery talks, Thompson sampling ML, metabolomics chromatography, and a Conway interview), but one substantive item emerges: a 2024 arXiv paper (2408.16263v2) extending McKay-Thompson series to "defect" versions, preserving genus-zero Hauptmodul structure. | MATH: Classical McKay-Thompson series T_g(q) = q^−1 + O(q) for g ∈ 𝕄 (Monster group) are Hauptmoduln for genus-zero subgroups of SL(2,ℝ). The new work (Lin–Shao 2021, extended in 2408.16263) constructs twined partition functions Z_g(τ) for defect lines in the Monster CFT, requiring modular invariance groups that are still genus-zero. Key constants: the Monster order |𝕄| = 808017424794512875886459904961710757005754368000000000 ≈ 8.08 × 10^53; the minimal faithful representation dimension 196883; the identity element gives T_1(q) = j(q) − 744 where \( j(q) = q^{-1} + 196884q + 21493760q^2 + Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -