Abstract
<jats:p>This update (v2) adds the resolution of the effective matter density problem within the UAT/UCP framework. The new document establishes the identity η ≡ κ_crit = 4.978, demonstrating that the Lagrangian vacuum minimum and the Ivancho causal limit are the same fundamental constant. Numerical integration of the Klein-Gordon equation reveals that the scalar field φ is frozen at ~9% of its minimum —an open puzzle that does not invalidate the mechanism. The causal membrane integral M_p = ∮ Ψ_8phase · κ_crit dt is derived from the surface term of the UAT action, showing that mass amplification depends on κ_crit as a structural constant, not on the dynamical field value. The amplification factor A = κ_crit × φ × (1 - 0.07) ≈ 7.49 yields Ω_m^(eff) = 0.3133, in 0.55% agreement with Planck 2018. Supplementary Python scripts for the Klein-Gordon integration and λ parameter sweep are included.</jats:p>