Dzhanibekov Effect in Quantum Topology: Unified Theory of Topological Phase Transitions

We establish a fundamental connection between the Dzhanibekov effect (classical instability of rigid bodies) and topological phase transitions in quantum geometry. The theory demonstrates that sphere-torus transi- tions (boson-fermion transmutations) obey identical dynamical equations to rotating bodies with intermediate inertia moments. Key results: (1) Anisotropic curvature singularities map to Dzhanibekov flips, (2) Quark confinement emerges as topological torque stabilization, (3) Black holes are frozen phase transitions. Experimental signatures in gravitationalwaves and quantum simulations are predicted.