Quantum Gravity in the GTE/Phi_MDL Framework: Functional Completeness

We establish perturbative quantum-gravitational completeness for the GTE/ framework across six benchmark criteria. The curved-background Lagrangian L[ ;g_μν] is uniquely determined by MDL minimality and the Wald entropy argument, with ξ = 0 forced by three independent arguments, and the Einstein field equations G_μν = 8π GT_μν[ ] follow as a derived consequence. UV finiteness on arbitrary smooth curved backgrounds is established via DeWitt-Schwinger heat-kernel and Hadamard propagator analysis: curved-background UV contributions reduce to finite Planck-scale renormalizations, leaving no UV problem beyond flat spacetime. Five mutually equivalent descriptions of the GTE encoding structure (Lagrangian, Reed-Solomon code, holographic/RT, MDL, and QEC) are proved equivalent in the GTE Holographic Encoding Theorem (all twenty directed implications closed). The SM generation orbit is a Reed-Solomon [5,3,3]_7 code over GF(7) ( , zero sorry); the area unit a^2 = 4 _ Pl^2 7 is algebraically determined. The MDL-minimal initial state (flat, field-kinetic-dominated, log_2 3 ≈ 1.585 bits of initial data) dissolves the horizon, flatness, and domain-wall problems without inflation; a quantum bounce is predicted at Planck density. The conditional prediction n_s = 1 - (2)/(2π^2) = 0.96488 (0.004σ from Planck~2018) requires the EFE-bridge step. The tensor-to-scalar ratio r = 0 is the primary falsifiable prediction for LiteBIRD. The dark-energy fraction Ω_Λ = 0.6899 matches observation at +0.18σ from Planck~2018 (conjecture; quantum mechanism open).