Deformation Quantization of Cl(∞, 0) and Rational Period Quantization of Reversion-Invariant Hodge Classes

Abstract

We establish an unconditional geometric-topological resolution of the Hodge Conjecture for algebraic varieties mapped into the infinite-dimensional real Clifford algebra Cl(∞, 0) over the Pascal Spindle Horn Cyclide horosphere H². By endowing Cl(∞, 0) with a smooth Kähler–Atiyah deformation quantization, we prove that every harmonic (k, k)-form class invariant under Clifford reversion A ↦ A† corresponds to a torsion-free parallel section under Cartan's Exterior Differential Systems. Furthermore, we demonstrate that the period integrals of these reversion-invariant classes over closed topological cycles are strictly rational, ∫ᵧ ω ∈ ℚ, constrained by the nilpotent horizon Calabi–Yau volume capacity V_cap = ζ(6) = π⁶/945. This constructs an explicit algebraic cycle representation without singular locus blow-ups, unifying deformation quantization with classical algebraic topology.