Eleven Fundamental Constants from E8 Boundary Geometry: The Fine-Structure Constant, Three Gauge Couplings, Four Gravitational Quantities, the Cosmological Constant, and the Electron Mass from One Root Lattice
Eleven Fundamental Constants from E8 Boundary Geometry: The Fine-Structure Constant, Three Gauge Couplings, Four Gravitational Quantities, the Cosmological Constant, and the Electron Mass from One Root Lattice
We derive eleven fundamental constants of nature from a single mathematical object: the E8 root lattice of the E8×E8 heterotic string at level k=1. The four inputs are exact properties of E8: dimension 248, root length |α|²=2, dual Coxeter number h*=30, and central charge c=8. No free parameter is introduced at any step. The eleven predictions are: the Thomson-limit coupling α⁻¹=137.035999086 (0.11 σ, CODATA 2018); the electroweak coupling α⁻¹(Mz)=127.952496 (0.55 σ); the Weinberg angle sin²θw(Mz)=0.231222 (0.06 σ); the strong coupling αs⁻¹(Mz)=8.530 (0.67 σ); the AdS radius L=(16/3)l_Pl; the Hawking temperature T_H=T_Pl/(8π) (exact); the Bekenstein entropy S=4π (exact); the GUT Weinberg angle 3/8 (exact); the cosmological constant Λ_Pl=e^(-2α⁻¹)/324 (0.20%, within CMB uncertainty); the gravitational coupling α_G=Λ_Pl^(3/8 - (11/12 + ε/4)α) (0.12%); and the electron mass m_e=m_Pl√α_G=0.51130 MeV (0.060%, CODATA 2018). All predictions are triple-audited.