The Θ–Ψ Framework: and the Frozen Bulk Mode (Paper II): Geometric Stabilization and the Kepler Attractor

In Paper I, we presented observational evidence that the largest cosmic voids are 4–5σ rounder than ΛCDM predictions, along with correlations to the CMB Cold Spot, Hubble dipole, and 120 Mpc quasi-periodic signal. Here we derive the exact analytic solution for the frozen bulk scalar field: Θ(r) = Θ₀ tanh(κr) with soft-wall scale κ⁻¹ ≈ 55 Mpc, and prove that the universe asymptotically approaches the Kepler packing limit: Ω_void → π/(3√2) ≈ 0.74048 This is a mathematical theorem (Hales 2005), not a fitted parameter. Present-day observations (Ω_void ≈ 0.740 ± 0.012) indicate the system is ~80–90% relaxed after 13.8 Gyr, evolving toward this unique attractor over a timescale: τ_relax ~ 50–100 Gyr derived from κ⁻¹ and Hubble friction with no free parameters. Key Theoretical Results: Exact field solution: Stable tanh(κr) kink separating void/structure regions Product ansatz: Multi-void configurations maintain field boundedness (|Θ| ≤ Θ₀) Recombination as geometric phase transition: Baryons encounter frozen Θ gradients at z ≈ 1100, producing abrupt void topology (not gradual gravitational evacuation) CMB Cold Spot mechanism: Deepest Θ-null produces enhanced ISW effect (ΔT ≈ −70 μK) Falsifiable Evolutionary Predictions: Ω_void(z): Should increase from 0.72 (z=3) → 0.740 (z=0) → 0.743 (z=−1) Void ellipticity e(z): Should decrease from 0.19 (z=3) → 0.11 (z=0) → 0.08 (z=−0.5) 120 Mpc signal: Should sharpen over time (not redshift away like BAO)