Spectral–Geometric Separation in Gapped Lindbladian Invariant Manifolds

We construct two finite-dimensional Lindbladian models possessing exact two-dimensional invariant manifolds. For both systems, we derive closed-form steady states, concurrence, and complete Liouvillian spectra. In each case, the Liouvillian gap remains constant under coherent perturbation, while the steady state deforms continuously within the invariant manifold. Entanglement decays asymptotically without any spectral closing. These results demonstrate a structural separation between spectral contraction strength and steady-state entanglement geometry in invariant Lindbladian systems.