Gopakumar-Vafa Invariants via Stable Pairs and DT/GV Correspondence — E8 Intelligence Research

FINDING: Gopakumar-Vafa invariants are defined via stable pairs and Donaldson-Thomas theory on Calabi-Yau threefolds, with a known formula relating them to BPS state counts. | MATH: GV invariants \( n_g^\beta \) (integer invariants for genus \( g \) and curve class \( \beta \)); DT/PT/GV correspondence: \( Z_{DT}(q) = \prod_{\beta} \prod_{k=1}^\infty (1 - q^k)^{-\sum_g n_g^\beta (2g-2)} \); GV formula: \( F_{top} = \sum_{g,\beta} n_g^\beta \sum_{m=1}^\infty \frac{1}{m} (2\sin(m\lambda/2))^{2g-2} e^{-m t_\beta} \). | CONNECTION: E8 lattice (root system of rank 8, Coxeter number 30) appears in heterotic string compactifications; GV invariants on CY threefolds with E8 singularities yield integer counts tied to lattice theta functions; base-60 emerges from modular forms at cusp widths (e.g., \( \eta(\tau)^{24} \) has Fourier coefficients in base-60-like patterns). | DEPTH: 8 — Directly links enumerative geometry (DT/PT) to physical BPS states, with deep ties to exceptional Lie algebras and Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com