Deriving General Relativity from a Bilayer Field on S3 - Angular World Architecture - (Gravitational Sector)

Deriving General Relativity from a Bilayer Field on S³ — Angular World Architecture (Gravitational Sector) General relativity is the most successful theory of gravity ever constructed: light deflection, Mercury's perihelion precession, gravitational waves, and the M87 black-hole image confirm Einstein's equations to extraordinary precision. Yet GR retains three structural gaps that a century of effort has not closed: the inevitability of singularities (Penrose–Hawking theorems), the destruction of quantum information at black-hole horizons (the information paradox), and the 4. 9σ discrepancy between local and cosmological measurements of H₀ (the Hubble tension). This article shows that all three gaps find natural resolution when gravity is treated not as a fundamental force, but as the long-wavelength limit of a nonlinear bilayer field Φ/Φ̄ living on the 3-sphere S³. Einstein's equations G_μν = (8πG/c⁴) T_μν are derived from the master equation via the Deser uniqueness theorem — they are consequences of the bilayer dynamics, not independent postulates. Black holes are reinterpreted as dissipative solitons: they have finite curvature everywhere, information is encoded in bilayer deformation modes, and the Hawking temperature marks the edge of information recovery, not destruction. The Hubble tension is addressed by a geometric coupling αL = Ωb / (Ω_Λ · π · η), with η = √Ξ (1+Ξ), that predicts the local H₀ = 73. 01 km/s/Mpc from the cosmological H₀ = 67. 40 km/s/Mpc with zero free parameters. Gravitational-wave polarizations follow from the SO (4) symmetry of S³ — exactly two tensor modes, scalar and vector modes forbidden — consistent with 90 LIGO/Virgo events. The matter density parameter Ωₘ = 1/π is derived from the Hopf fibration topology (Planck 2018: 0. 315 ± 0. 007; agreement within 0. 5σ). In total, 56 general-relativistic results are presented with explicit derivation status: 52 formally derived (D) and 4 empirically supported at ≤ 2σ (S). This article constitutes the gravitational sector of a broader unification programme. In the companion paper AWA-QM and the AWA-Unification paper, quantum mechanics emerges as the ξG → 0 limit and general relativity as the ξG → 1 limit of a single bilayer field equation on S³, with ξG = 2 (m/mP) ² as the continuous bridge parameter. Five falsifiable predictions are identified, testable by LISA, XRISM, JWST, and next-generation AGN surveys (2025–2035). Limitations — including the absence of numerical galaxy rotation curves — are stated explicitly. Keywords: general relativity, topological solitons, 3-sphere, bilayer cosmology, black-hole information paradox, Hubble tension, gravitational waves, matter–antimatter, dark energy, Hopf fibration, Angular World Architecture, AWA.