Quantum Gravity in the GTE/PhiMDL 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, 3₇ code over GF (7) (, zero sorry) ; the area unit a² = 4Pl² 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 Z₇ wall network formed at the ordering crossover TG 0. 70 GeV is annihilated by the canonical coupling bias well before nucleosynthesis, leaving no surviving defect network. The conditional prediction nₛ = 1 - (2) / (2²) = 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 OmegaLambda = 0. 6899 matches observation at +0. 18 from Planck 2018 (conjecture; quantum mechanism open).