We present a coordinate-free proof of the Poincaré Conjecture and the classification of closed 3-manifolds by embedding 3-dimensional Riemannian manifolds into the infinite-dimensional Clifford algebra Cl(∞, 0) over the isotropic horosphere H². We show that Hamilton's Ricci flow ∂gᵢⱼ/∂t = -2Rᵢⱼ translates under Spin(4) ≅ Spin(3) × Spin(3) to a continuous bivector rotor gauge evolution. Rather than encountering finite-time neck-pinch singularities that require manual topological surgery (as in the classical Hamilton–Perelman framework), localized curvature concentrations undergo conformal annihilation at the Nilpotent Horizon (n_∞² = 0). Driven by the irrational phase torque ratio θ = log₂(3) ∉ ℚ and bounded by the Calabi–Yau metric volume ceiling V_cap = ζ(6) = π⁶/945, any simply connected closed 3-manifold M³ relaxes smoothly and monotonically to the uniform round 3-sphere S³ without singular blow-ups.