CoreLumen IV: Black Holes in the Asymptotic R3 Background — Static Strong-Curvature Basin Structure (Zenodo Archival Reference Edition v2.0)

This archival volume establishes Regime R4 of CoreLumen Cosmology as the static and stationary axisymmetric strong-curvature sector embedded in an asymptotic R3 background. We derive the closed Einstein–matter system for the amplitude–phase field Ψ = ρeiθ under Structural Charter v1.0 conditions (Zρ > 0, Zθ > 0, c_s^2 > 0, c_T = 1) together with dynamical vacuum sequestering. Horizon regularity enforces critical-point anchoring (ρ_h, θ_h) ∈ C_U, so event horizons act as phase-basin selection surfaces. For multi-basin potentials this induces discrete branch structure and a constrained shooting problem. Interior scaling classes are classified structurally, including Kretschmann growth behavior. In asymptotic de Sitter embeddings, two-horizon basin-mismatch configurations give rise to phase-wall channels with minimal thermodynamic implications. The anchoring mechanism is extended to Kerr geometry through near-horizon degeneracy analysis, preserving discrete branch structure in stationary axisymmetry. All results are regime-local and conditional on effective-field validity. No ultraviolet completion, singularity resolution, or information-loss resolution is claimed.