No External Model Selection in Quantum Gravity Records, Diffeomorphism Redundancy, and the Necessity of Non-Effective Internal Selection

We apply the No External Model Selection (NEMS) classification framework to quantum-gravity completions by fixing a minimal gravitational record language and isolating quantum-gravity structure that forces record-level non-categoricity absent internal selection. The main result is a theorem package: (i) a minimality lemma for the gravitational record fragment ; (ii) a quantum-gravity non-categoricity theorem establishing (_;) >1 under explicit, framework-neutral gravitational premises unless internal selection is already present; and (iii) a Class IIb consequence under the NEMS closure bundle (single actuality on records, no external model selection, no free completion bits, and diagonal-capable self-reference). We provide two complementary mechanisms for non-categoricity: Route A (relational/gauge anchoring multiplicity) and Route B (horizon/complementarity reconciliation multiplicity). The result is a conditional but sharp constraint on the semantic architecture of any closed, definite, computationally universal quantum-gravity completion relative to the minimal record fragment. The domain of discourse is the class of quantum-gravity completions admitting a finite law-description, stable semiclassical record regions, and sufficient computational universality for diagonal self-reference; no specific QG formalism (string, loop, causal set, etc. ) is presupposed. Trust boundary. Class IIb and record-level conclusions are conditional on the stated QG premise bundle; the classification engine remains Paper 2, with formal companions in nems-lean. See.