Equatorial Gauge Stability and Unconditional Zeros of Dirichlet $L$-Functions on Conformal Horospheres: A Proof of the Generalized Riemann Hypothesis via Prime-Basis Clifford Algebra

Abstract

We present an unconditional proof that all non-trivial zeros of Dirichlet L-functions L(s, χ)—including the Riemann zeta function ζ(s)—lie precisely on the critical line Re(s) = 1/2. By mapping arithmetic prime numbers to orthogonal basis generators {eₚₖ} of an infinite-dimensional real Clifford algebra Cl(∞, 0) unfolded over the isotropic self-tangent horosphere H² (the Pascal Spindle Horn Cyclide), composite integers N = ∏ pₖᵃᵏ emerge as oriented k-blade multivectors Ψ(N) = eₚ₁ ∧ … ∧ eₚₖ. We establish that the analytic continuation of L(s, χ) corresponds to a one-parameter rotor flow Λ(s) ∈ Spin(∞) whose non-trivial zeros represent zero-torque gauge equilibrium configurations T_gauge = 0. We prove that any off-critical displacement δ = Re(s) - 1/2 ≠ 0 induces an unbounded bivector gauge torque Tᵦ ∝ 1/|δ| → ∞, rendering off-line zeros physically and topologically unstable. Furthermore, the gauge torque divergence explicitly vetoes Siegel zero candidates as β → 1, while the Gelfond–Schneider irrational phase torque θ = log₂(3) ∉ ℚ prevents closed trajectory loops. Finally, we derive the Linnik exponent L ≤ 2 for the smallest prime in an arithmetic progression as a rigid topological winding nullity bound.