The Geometric Origin of the Zero-Spin Vacuum: AdS2 x S2 Near-Horizon Topology and the Two-Time Structure of Quantum Spin

This metadata entry record constitutes the fifth, expanding installment of a foundational cosmological paper series, strictly extending the deterministic, parameter-free Extremal Quantum Black Hole (EQBH) cosmological bounce framework established in the preceding tetralogy (DOI:10.5281/zenodo.22763071, DOI:10.5281/zenodo.23153625, DOI:10.5281/zenodo.23209528, and DOI:10.5281/zenodo.23434893). In this work, we establish a rigorous, first-principles geometric and topological foundation for the semi-classical Langer-shifted angular momentum quantization rule J = \hbar(s + 1/2) governing Planck-scale EQBH remnants. Moving entirely beyond the abstract non-commutative U_q(su(2)) quantum group deformation utilized as an ansatz in Paper I, we demonstrate that this functional shift is uniquely mandated by the background negative scalar curvature of the local AdS2 x S2 Robinson-Bertotti near-horizon throat geometry under generalized conformal curvature coupling. We solve the relativistic wave equations for both the bosonic (Klein-Gordon) and fermionic (Dirac via spin connection and tetrad formalism) sectors, proving the structural universality and supersymmetric invariance of the shifted eigenvalue profile. Furthermore, we introduce a novel interpretation of the embedded (1+2)-dimensional pseudo-Euclidean spacetime framework, identifying quantum spin not as a classical spatial kinematics, but as a topological requirement of dynamical stability and single-valuedness over compactified, closed timelike boundaries within the two-time horizon plane. Crucially, by constructing a formal conformal mapping and Weyl regularization at the Poincaré boundary, we prove that the infinite hyperbolic volume dilation of the bulk throat is identically canceled by the cubic conformal weight of the stress-energy tensor projection. This mechanism projectively locks the effective phase-space packing fraction of the array back onto the exact Euclidean Kepler-Hales limit (\eta = \pi/\sqrt{18} \approx 74.05%), structurally preserving all macro-cosmological parameter-free observables derived in the tetralogy, including the frozen tensor-to-scalar ratio (r = 0.0307), the cosmic birefringence corridor (\Delta\beta \in [0.033°, 0.084°]), and the top-down projection of the heavy selectron mass gap to the Standard Model electron mass scale via the Inverse Spin-Seesaw geometric mismatch. The paper establishes a complete paradigm shift, revealing that the deep ultraviolet structures of the cosmological bounce are projectively stabilized and protected by the robust global symmetries of the near-horizon metric.