Resolution of the Galactic Feedback Paradox and Ultra-Fast Outflows: Substrate Acoustic Confinement and Torsional Relaxation Pulses in an Elastically Pre-Stressed Continuum

Cosmological hydrodynamical simulations of galaxy formation within ΛCDM require aggressive stellar and active galactic nucleus (AGN) feedback to prevent overcooling. However, observations reveal a dual empirical paradox: (i) in dwarf galaxies, supernova blast waves vent through porous interstellar chimneys with minimal coupling, leaving neutral gas discs unperturbed and exhibiting mass-loading factors an order of magnitude lower than models require; and (ii) in active galactic nuclei, X-ray spectroscopy of Fe XXV/XXVI lines detects Ultra-Fast Outflows (UFOs) with mildly relativistic velocities (v ~ 0.1–0.3 c) and momentum rates exceeding the single-scattering radiation limit (p_dot > L_bol / c). Building upon our unified framework of the physical vacuum as an elastically pre-stressed continuum, we show that these phenomena are governed by the acoustic-elastic coupling between baryonic solitons and the substrate. Localized supernova kinetic energy dissipates into acoustic shear waves of the continuum rather than macroscopic gas expulsion, preserving dwarf galactic gas discs. Simultaneously, relativistic UFOs emerge as collimated torsional shear relaxation pulses produced when the central accretion vortex relieves non-linear winding stress, naturally scaling outflow velocities to the substrate shear wave speed (v_UFO ~ (G_v / ρ_0)^1/2 ≈ c). We derive the analytical feedback containment and outflow energetics, resolving the cosmic feedback paradox under Occam's razor.