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 \( n_g^β \) (integer invariants for genus \( g \) and curve class \( β \)); DT/PT/GV correspondence: \( ZDT(q) = ∏β ∏ₖ₌₁^∞ (1 - q^k)-∑_g n_g^β (2g-2) \); GV formula: \( Fₜₒₚ = ∑g,β n_g^β ∑ₘ₌₁^∞ 1/m (2sin(mλ/2))²ᵍ⁻² e-m t_β \). | 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., \( η(τ)²⁴ \) 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