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) / framework from zero-parameter first principles, with central algebraic steps certified in Lean~4. The dark-energy fraction is fixed by two independent structural routes: PSC route: = 0.6899 (+0.18σ from Planck~2018; ); holographic route: = 3π/14 = 0.6732 (-2.8σ); together these bracket Planck~2018, and N_ gen = 3 is the unique integer for which both routes simultaneously bracket ( ). The associated energy density ρ_Λ = (9/112) ^2 H_0^2 agrees with observation at the few-percent level; a PSC boundary condition fixes w = -1. The vacuum is anomaly-free (machine-certified, zero ), and holographic mode counting (3L rather than L^3) suppresses one-loop vacuum corrections by ≈ 10^-42. The baryon-to-photon ratio is derived via the kink–top coupling (FKTT): η_B = 6.109×10^-10 (+0.15σ from Planck~2018/BBN (6.10±0.06)×10^-10; , zero sorry, zero axioms). Further predictions from the same integer inputs include: the CMB spectral index n_s = 1 - 2/(2π^2) = 0.96488 (0.004σ,~ , fourteen Lean theorems); the tensor-to-scalar ratio r = 0 exactly (no primordial gravitational waves; primary LiteBIRD falsifiable prediction); the neutrino mass sum Σ m_ν = 59.4meV; the CKM CP phase δ_CP = 68.51^ (0.017\% from PDG); and the Hubble constant H_0 = 67.95km/s/Mpc ( ; T_ CMB = 2.7255K is the sole external input). An explicit falsifiability profile is provided.