Non-Equilibrium Holographic Brane Cosmology in AdS5. I-D: Stochastic Moduli Freeze-Out, Non-Supersymmetric Standard Model Vacuum Cancellation, and Radion Stabilization

A complete quantum theory of cosmology must explain not only the algebraic unitarity of the de Sitter horizon (Paper I-A), the elimination of the initial Big Bang singularity (Paper I-B), and the infrared stability of the massive graviton spectrum (Paper I-C), but also the microscopic origin of the four-dimensional fundamental constants—most notably the 10^(-122) M_Pl^2 hierarchy of the cosmological constant—without invoking anthropic selection over an unobservable multiverse landscape. In this fourth and final paper of the series (Paper I-D), we formulate the dynamical selection of the four-dimensional vacuum and prove its ultraviolet quantum stability in the presence of the full non-supersymmetric Standard Model. First, we demonstrate that during the five-dimensional quantum bounce of a Karch-Randall 3-brane nucleated by a collapsing Schwarzschild-AdS5 progenitor of mass M_5, the four-dimensional couplings (Lambda_4, M_Pl, alpha_i, v_EW) evolve as dynamical moduli fields driven by a Tolman-redshifted Hawking thermal bath T_eff(tau) = R_+ / (pi * L_5 * a(tau)). We prove that the governing overdamped Langevin stochastic differential equation possesses strictly additive noise in moduli space, rendering the Ito and Stratonovich prescriptions identical and driving the associated Fokker-Planck probability density toward cosmological freeze-out as a(tau) >> a_min. Second, combining the five-dimensional Bekenstein-Hawking microstate entropy S_BH^(5) ~ M_5^(3/4) with the Euclidean Vilenkin-Linde tunneling instanton I_inst = mu / Lambda_4, we derive a normalizable inverse-gamma-type probability distribution P(Lambda_4) whose analytical mode peaks at Lambda_(4,peak) ~ M_Pl^2 / S_BH^(5) ~ 10^(-122) M_Pl^2 upon saturating the hyperfinite Type II_1 von Neumann algebra bound. Finally, performing zeta-function regularization over the 28 bosonic and 90 fermionic degrees of freedom of the Standard Model, we prove that top-quark dominance (rho_ren^mat ~ -10^(-64) M_Pl^4) is dynamically absorbed in counter-phase by the quantum Israel junction conditions and the holographic bulk Casimir-Weyl response, leaving an uncompensated residue |delta Lambda_UV| <= 10^(-130) M_Pl^2 while stabilizing the radion above the Breitenlohner-Freedman bound (m_rad^2 > 0).