Cosmological Predictions of the GTE/Phi_MDL Framework: Dark Energy, the CMB Spectral Tilt, and Gravitational Signatures from First Principles

We derive the principal cosmological observables of the Generative Triple Evolution (GTE) / Phi_MDL framework from zero-parameter first principles and certify the central algebraic steps in Lean 4. The observed dark-energy fraction is fixed by two structurally independent routes: a Perfect Self-Containment (PSC) reflexive-closure count giving Omega_Lambda = (ln(2)/3*pi)*log_2(2000/3) = 0.6899 (0.71 sigma from Planck 2018), and a three-tape holographic mode count giving Omega_Lambda = tau*(pi/2) = 3*pi/14 = 0.6732, with the proper-time rate tau = 3/7 derived from Rule-110 ether dynamics. The two routes bracket the observed 0.6889 from above and below; the 2.4% spread is irreducible (the two underlying constants are distinct transcendentals). The associated energy density obeys rho_Lambda = (9/112)*M_Pl^2*H_0^2, agreeing with observation at the few-percent level; a PSC boundary condition fixes the equation of state at w = -1, evading the obstruction that defeats holographic dark energy. Holographic mode counting (3L modes, not L^3) suppresses one-loop corrections by approximately 10^{-42} relative to the standard estimate, addressing the quantum-protection question. We further derive the CMB scalar spectral index n_s = 1 - ln(2)/(2*pi^2) = 0.96488 (0.004 sigma from Planck 2018) from a binary holographic running rate, certified by fourteen zero-sorry Lean theorems; the Newton-constant normalization from a discrete Ollivier-Ricci (Gorard) curvature chain (k_SD = 10/13); Hawking emission as kink radiation near the BPS critical mass M_kink_crit = 290.10 MeV; a strong-field ultraviolet bound V_max = 2m^2/49; the neutrino sum Sigma m_nu = 59.4 meV; and the CKM CP phase delta_CP = pi/2 - 3/8 = 68.51 degrees (0.017% from PDG). All central results are machine-checked in Lean 4 with zero sorry. We give an explicit falsifiability profile.