Spin as a Geometric Pseudovector: Dzhanibekov-Topology Correspondence in Quantum Systems

We establish a fundamental correspondence between the Dzhanibekov effect (classical rotational instability) and spin dynamics in anisotropic quantum systems. The theory demonstrates that spin flips governed by the Landau-Lifshitz equation with intermediate anisotropy coefficients represent quantum analogs of topological phase transitions. Key results: (1) Spin emerges as a geometric pseudovector from toroidal curvatureholonomy, (2) Intermediate anisotropy in γ(Kx − Kz ) corresponds to topological torsion, (3) Experimental signatures in quantum dots and superconducting circuits confirm pseudovector nature. This provides a unified geometric mechanism for spin-statistics, quark confinement, and gravitational phase transitions.