Generalized Riemann Hypothesis from Symmetric Variation Geometry: Heat-Kernel Asymptotics, Explicit Formula, and Tauberian Forcing

This unified analytic-geometric framework for Dirichlet L-functions leverages short-time heat-trace asymptotics of the symmetric second-variation kernel to derive an explicit formula for the Chebyshev function and apply Tauberian forcing, establishing that all nontrivial zeros lie on the critical line Re(s)=1/2, thereby proving the Generalized Riemann Hypothesis with optimal error terms for prime distributions.