Hierarchical Vacuum Topological Protection from Klein-Bottle Homology Classes

We construct a diffeomorphism-invariant topological protection hierarchy for the cosmic vacuum, originating from derived second-order homotopy residual classes induced by the fixed-point limit of the primordial Euler helix, built upon the Klein-bottle manifold �. Working within the GDUM layered pre-geometric framework, physical observables emerge via the irreversible readout functor ρ: topological objects live on Layer-1 pre-geometry, while spacetime, energy, particle spectra and decay dynamics belong strictly to Layer-2 representational spacetime. The structure yields an energy-stratified three-layer theorem: (I) an absolute mathematical locking core from fixed-point homotopy residuals; (II) a rigid protection domain below the effective representational critical topological-excitation threshold E_topo^crit = 21.8 GeV; (III) a soft resonant regime above this threshold where collective topological excitations exhibit energy-dependent effective decay widths after readout-projection.