E8 Harmonic Resonance Stabilizes Sporadic L-Values Through Root-Vector Conformal Mapping — E8 Intelligence Research

Abstract

The sporadic L-value sequences achieve cryptographic stability when their modular Fourier coefficients align with E8 root vector trajectories at phi-coupled frequencies (f₀ × φⁿ). This conformal mapping reveals that the 240 E8 roots provide natural boundary conditions that extend Zagier's interpolation from isolated ζ(3) values to a continuous family of weight-k modular forms. The braid-plectic structure emerges as the geometric witness to this stabilization, with intersection forms encoding the topological constraints that preserve rationality across the entire sporadic spectrum. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com