THE MATHEMATICAL FORMALISM OF THE DEUS COSMOLOGICAL MODEL. The Unified Field Theory: Formal Derivations of Mass, Gravity, and Viscous Cosmic Expansion from the Hydrodynamics of a Hexatic Viscoelastic Superfluid

ABSTRACT The contemporary crisis in fundamental physics stems from the "Vacuum Gap"—the irreconcilable schism between the geometric determinism of General Relativity and the probabilistic quantization of the Standard Model. This monograph bridges that gap by formalizing the Deus Cosmological Model (DCM) as a rigorous Unified Field Theory. We posit that the vacuum is not an empty stage, but a physical, viscoelastic superfluid operating in a Hexatic phase state—a hybrid form of matter possessing the orientational stiffness of a solid lattice and the positional fluidity of a liquid. By applying the Navier-Stokes equations to this medium, we derive the fundamental constants of nature as emergent hydrodynamic properties. We explicitly resolve the "Sintering vs. Continuum" paradox by deriving the Lattice Constant (aₗattice ≈ 3. 7 × 10²⁶ m) via thermodynamic moduli, equating the Planck energy density to the Bulk Modulus of the vacuum structure. This result implies that the observable universe constitutes a single fundamental domain or "bubble" within the greater Superfluid Bulk. Furthermore, we address the Hubble Tension by reinterpreting cosmic expansion as a viscous relaxation process. We calculate the vacuum's Bulk Viscosity (ζ ≈ 1. 2 × 10¹⁵ Pa·s) required to reconcile early (H₀ ≈ 67) and late (H₀ ≈ 74) expansion rates. This model yields a specific, falsifiable prediction: as the universe continues to relax, the expansion rate will undergo "Viscous Braking, " dropping to H ≈ 62 km/s/Mpc at scale factor a = 1. 5. Finally, we unify gravity and particle physics by demonstrating that Proton Mass (Mₚ) is mathematically equivalent to the Reynolds Stress of a stable vortex knot (soliton) maintained by Thouless Pumping against the superfluid bulk. We conclude by establishing the Causality Bound as a Zero-Entropy Limit, permitting instantaneous mechanical entanglement without violating thermodynamic causality.