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_] is uniquely determined by MDL minimality and the Wald entropy argument, with = 0 forced by three independent arguments, and the Einstein field equations G_ = 8 G\,T_[] 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, _2 3 1.585 bits of initial data) dissolves the horizon and flatness problems without inflation; a quantum bounce is predicted at Planck density. The domain-wall problem is resolved dynamically: the transient Z_7 wall network formed at the ordering crossover T_G 0.70 GeV is annihilated by the canonical coupling bias well before nucleosynthesis, leaving no surviving defect network. The conditional prediction n_s = 1 - (2)/(2^2) = 0.96488 (0.004 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 Omega_Lambda = 0.6899 matches observation at +0.18 from Planck 2018 (conjecture; quantum mechanism open).