Defect McKay-Thompson Series and Genus-Zero Monstrous Moonshine — E8 Intelligence Research

FINDING: Defect McKay-Thompson series for the Monster CFT generalize the genus-zero property of Monstrous Moonshine to twined partition functions with line defects inserted. | MATH: T_g(q) = Σ tr(g|V_n) q^n forms Hauptmoduln for genus-zero subgroups Γ_g ⊂ SL(2,ℝ); Lin–Shao (2021) construct defect-twined analogues Tg,D(q) where D is a topological line defect, conjecturally also Hauptmoduln. Modular invariance group of the defect theory constrains the series. | CONNECTION: Genus-zero condition ↔ modular curve X(Γ_g) has genus 0 ↔ rational parametrization by a single Hauptmodul; the Monster's 194 conjugacy classes map to 171 distinct genus-zero groups (Thompson). Moonshine coefficients encode dimensions of Monster irreps: 196884 = 196883 + 1, where 196883 is the smallest nontrivial Monster irrep dimension. These integers relate to the Leech lattice (24-dim even unimodular, no roots) and its automorphism group Co_0 → Monster. | DEPTH: 9 --- **1. Key mathematical insight** The 1992 Mo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com