Horizon Phase Transitions and the Resolution of the Black Hole Information Paradox: A Deterministic Continuum Formulation within the Symmetry-Ordered Superfluidity (S.O.S.) Framework

We review the long-standing black hole information loss paradox by reformulating the pseudo-Riemannian geometry of event horizons as a local, non-dissipative fluid-dynamic phase transition within the Symmetry-Ordered Superfluidity (S.O.S.) framework. By tracking the four-divergence of the covariant Bohm-Santos quantum stress tensor Qµν across collapsing boundaries, we demonstrate that the traditional geometric null hypersurface is replaced by a physical boundary layer of finite thickness governed by an ultraviolet scale cutoff δ = ϵlP /Ω0. Madelung quantum hydrodynamics shows that mass-energy entering the horizon avoids the unphysical spatial singularity (r → 0) and stabilizes deterministically at a central saturation core density ρ(0) = ρ0/2, completely suppressing gravitational gradient blow-ups and bounding the Kretschmann scalar globally (KSOS < ∞). Information conservation is rigorously preserved within scale-critical homogeneous Besov spaces B˙ 0 ∞,∞(R 3 ) through an invariant non-dissipative velocity profile vθ(r) ∝ r −ϕ −1 governed by the inverse Golden Ratio. Evaporation via Hawking radiation emerges as an acoustic phase-retarded transport wave (cs/c = 10−7 ), mapping internal states back onto the exterior domain with strict preservation of quantum unitarity (wSOS ≡ −1). (...)