Degeneracy of the Garriga–Mukhanov Perturbation Variables at Time-Symmetric Surfaces

This preprint identifies a domain-of-validity failure in the Garriga-Mukhanov perturbation variables for curved cosmological models at time-symmetric surfaces, where the Hubble rate and background field velocity both vanish.It derives a universal inverse-square divergence in the relevant curvature quantity, shows how the resulting second-order reduction develops an unbounded tower of apparent wrong-sign coefficients, and demonstrates through a canonical closed FLRW example that regular perturbation variables evolve smoothly through the corresponding poles.The work does not claim general ghost freedom. It establishes that the sign obtained from the singular reduced normalisation cannot be interpreted as an invariant kinetic norm in this regime.This record includes the preprint, LaTeX source, figure, verification script, numerical output, README, and checksums. The numerical results and figure are reproducible with a single Python command.