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 (+0.18 from Planck 2018; ); holographic route: = 3/14 = 0.6732 (-2.8); together these bracket Planck 2018. We prove that this bracketing is structural, not coincidental: the holographic value is the price of the MDL-minimal self-description carrier (a lower bound) and the PSC value is the capacity ceiling of the same adjudication ledger (an upper bound), with the inter-route ordering reducing to the machine-certified GTE-atom inequality 14(2000/3) > 9^2 (). The exact realized fraction is a left-computably-enumerable real of Turing degree 0' - definite but not computable - so no computable selection mechanism for exists, and the two routes are its computable endpoints; the census endpoint becomes a 3-decidable test at precision ^* 3.410^-4. The bracket is non-empty only for N_gen 3 (measurement-free); with the PSC Layer-I bound N_gen 3 this determines N_gen = 3 without Presentation Invariance (, conditional on named structural premises). The associated energy density _ = (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 sorry), and holographic mode counting (3L rather than L^3) suppresses one-loop vacuum corrections by 10^-42. A new defect-cosmology sector is derived: the order, restored after reheating, re-orders at T_G 0.70 GeV and forms a transient Kibble domain-wall foam; the canonical coupling ^2(D_)^2 (= 7/9, ) lifts the vacuum-label degeneracy and collapses the foam within \!10^-23 s - 700 before BBN - selecting the vacuum k = 0 and leaving zero surviving defect network (_GWh^2 310^-47 at f 0.02 Hz; N_eff 0), a parameter-free falsifiable prediction. The baryon-to-photon ratio is derived via the kink-top coupling (FKTT): eta_B = 6.10910^-10 (+0.15 from Planck 2018/BBN (6.100.06)10^-10; , zero sorry, zero axioms). Further predictions from the same integer inputs include: the CMB spectral index n_s = 1 - ln 2/(2π²) = 0.96488 (-0.005σ, CatAL, fourteen Lean theorems); the tensor-to-scalar ratio r = 0 exactly (no primordial gravitational waves; primary LiteBIRD falsifiable prediction); the neutrino mass sum m_ = 59.4\,meV; the CKM CP phase delta_CP = 68.51^ (0.017\% from PDG); and the Hubble constant H_0 = 67.95\,km/s/Mpc (; T_CMB = 2.7255\,K is the sole external input). An explicit falsifiability profile is provided.