Geometric Phase Transition, Half-Angle Tilt Resonances, and Topological Robustness in Open Centrifuge Manifolds

This revision establishes the complete topological framework for Revision 7 of theZolondo Program, incorporating a fundamental geometric phase transition under halfangle tilt configurations (θ ≈ 22.5° to 23.5°). By formalizing strict exchange symmetry(permutation invariance P_PB) between the photon polarization space (Poincaré sphere)and electron spin space (Bloch sphere), we resolve previous non-unitary leakageartifacts. Under high-frequency Floquet rotation, the system collapses to an effectivetime-independent Hamiltonian harboring non-Hermitian Exceptional Points (EPs). Weprove that while perfect alignment (θ = 90°) forms an unperturbed Decoherence-FreeSubspace (DFS), the half-angle interval modulates a non-Abelian Berry connection thatacts as a structural gauge filter. This filter forces an abrupt spectral narrowing of survivalamplitudes outside the singlet equator, mapping the boundary conditions of the Riemanncritical strip directly to stable open quantum system dynamics under dynamic Lindbladdephasing noise.