An Open Covariant Class of Linearly Spectrally Stable Two-Ended Wormhole Theories with a Q=2 Director Sector

This manuscript develops an enlarged class of local four-dimensional diffeomorphism-covariant theories admitting exact two-ended, asymptotically flat and horizonless wormhole backgrounds with a physical Q=2 director sector. The construction combines exact background reconstruction, a throat-regular reference-medium formulation, a dynamical timelike aether, and a global bundle treatment of perturbations. High-frequency stability is obtained through a small-coupling principal-symbol analysis ensuring ghost freedom, radial and angular gradient stability, and subluminal propagation. The low-frequency sector is treated globally on the physical perturbation bundle without assuming harmonic separation. A bundle-valued factorization of the spatial Hamiltonian, together with a positive covariantly generated zeroth-order operator, yields a self-adjoint nonnegative Hamiltonian with no negative L2 spectrum and no normalizable L2 zero mode. The stabilizing zeroth-order operator is realized as the second variation of a local covariant defect action using a global material chart and a smooth defect-map left inverse. The result establishes a nonempty open infinite-dimensional class of linearly spectrally stable covariant wormhole theories. Nonlinear stability, non-L2 threshold resonances, minimal field content, and observational optimization of the aether sector are not claimed.