Super-Oscillatory Deconvolution of Anomalous Interstellar Hyper-Chirps: Asymptotic Expansion of Degenerate Oscillatory Integrals and Metaplectic Filtering in Anisotropic Gelfand-Shilov Spaces

Mathematical Applications of Science Fiction We present a rigorous analytical framework for the deconvolution of anomalous "Hyper-Chirp" signals—transientwaveforms exhibiting non-linear instantaneous frequency modulation exceeding the Shannon-Nyquist limit—propagatingthrough dispersive interstellar media. By embedding the signal space into anisotropic Gelfand-Shilov spacesSμν (Rn), we construct a class of Metaplectic filters associated with the double cover of the symplectic groupM p(2n, R). We derive the asymptotic expansion of the associated degenerate oscillatory integrals where thephase function exhibits Ak -type singularities. The central result establishes the existence of a super-oscillatorydeconvolution kernel that resolves the wavefront set of the hyper-chirp in the microlocal limit ℏ → 0. Weprove five major theorems regarding the stability, convergence, and symplectic covariance of these operators,supported by ten fundamental lemmas. This work has profound implications for the detection of sub-Planckiansignatures in gravitational wave astronomy and crystalline quantum computing.