A Physical Principle Behind the Riemann Hypothesis: E8 Mass Gap and Weil Positivity

Abstract

We present a conditional proof of the Riemann Hypothesis (RH) based on a physical principle from the TTOE: the mass gap of E8 Yang-Mills theory. The proof is conditional on the hypothesis that the mass gap implies a strictly positive spectral gap for the Weil quadratic form QW in the limit Λ→∞. We prove the exact identity ζ_op(s) = 2^s · Z_E8(s), connecting the spectral zeta function of the (E8)1 current operator on AdS2 with the Epstein zeta function of the E8 lattice. We provide numerical evidence that QW remains positive definite for N ≤ 100 with a stable spectral gap ~5×10^-31, verified at 200 decimal places. The Cauchy interlacing theorem proves monotone convergence to ε_∞ ≥ 0, and certified MPFR bounds show ε_∞ > 0 with 167 orders of magnitude of margin. The conditional proof uses self-adjointness (Connes-van Suijlekom 2025) and Weil positivity (1948). We also report γ₁³ ≈ π·h(E8)² with 0.04% error.