Finite-Entropy Compressible Vacuum and Enstrophy-Driven Cosmological Relaxation: A Rigorous Hydrodynamic Formulation of Cosmic Acceleration and Invariant Spectra

The finite-entropy compressible vacuum framework establishes cosmic evolution as the hydrodynamic relaxation of an arithmetically bounded superfluid substrate, replacing dark energy and fine-tuned geometric parameters with rigorous fluid mechanics and topological invariants. Topological Spectral Cutoff: The discrete spectral resolution arises as the exact dimension of the two-form exterior algebra spanned by the fundamental ideal generators of the maximal class-number-one field, establishing a rigid cutoff that prevents high-frequency ultraviolet divergences without arbitrary parameter insertion. Covariant Hydrodynamic Expansion: Cosmic expansion and acceleration are derived via Buchert-Raychaudhuri kinematic spatial averaging of turbulent vacuum flows. Cosmic acceleration is driven by the positive-definite kinematic vorticity invariant, satisfying contracted Bianchi identities and preserving diffeomorphism invariance without an ad-hoc time-dependent cosmological constant. Lyapunov-Stable Enstrophy Relaxation: Vacuum enstrophy relaxation follows a stable logistic cascade governed by a balance between vortex stretching and multi-channel viscous dissipation. The system converges monotonically to a globally stable equilibrium attractor, eliminating finite-time blowup and providing a physical mechanism for the transition between early- and late-universe expansion rates. Hydrodynamic Virtual Inertia: Mach's principle is formalized through classical boundary-layer fluid mechanics. The inertial mass of a localized topological knot corresponds to the hydrodynamic added mass tensor generated by the reactive surface pressure of the displaced vacuum superfluid during acceleration. Turbulent Frame Drift and Casimir Ground State: The cosmic dipole anomaly reflects an accumulated kinematic velocity drift of matter relative to the vacuum acoustic rest frame, driven by integrated anisotropic turbulent Reynolds stresses. The residual ground-state tension corresponds to the modular automorphic invariant of the underlying Riemann surface. Solenoidal Vorton Regularization: Localized vorton dipole cores are regularized through divergence-free mollification, guaranteeing that the vorticity field satisfies the solenoidal condition everywhere without artificial source or sink singularities.