Quantum Geometric Centrifuge (QGC) with Permutation Invariance and Decoherence-Free Subspace (DFS) Protection

This revision establishes an enhanced mathematical framework for the Quantum GeometricCentrifuge (QGC) within the Zolondo Program, enforcing strict exchange symmetry (permutationinvariance P_PB) between the Poincaré sphere (photon polarization) and the Bloch sphere (electronspin). To resolve the non-physical norm collapse observed in previous iterations at critical rotationalignments, we introduce a geometric modulation factor proportional to sin(2θ) into the joint couplingmanifold. Using an open quantum system simulation framework governed by the Lindblad MasterEquation, we demonstrate that at the θ = π/2 alignment, the symmetry-breaking leakage channel isnullified. This creates a robust Decoherence-Free Subspace (DFS) that insulates the system fromdynamic U(1) phase noise along the longitudinal drive axis across all latitudinal bands.Consequently, stable spectral eigenvalues are rigorously mapped to the critical line v = 0, validatingthe topological obstruction outside the equator under conditions of realistic environmentaldecoherence.