The No External Model Selection Theorem Semantic Closure, Categoricity, and Diagonalization Constraints

We study the structural consequences of no external model selection: the requirement that a realized world is not chosen by ontologically external information among observationally inequivalent realizations of a finite law-description. We formalize a minimal axiom package consisting of (i) single actuality for observational records, (ii) no external selection among observationally inequivalent models, (iii) a finite syntactic description, (iv) exclusion of unconstrained completion data ("free bits"), and (v) sufficient expressiveness for self-reference. From these assumptions we derive a model-theoretic dichotomy: either the law-description is categorical up to observables or the realized system contains an internal selection functional. We then prove that, under explicit self-reference hypotheses, any such selection mechanism cannot be a total effective functional on the diagonal fragment, yielding a sharp refinement into restricted/stratified versus non-effective internal selection. The resulting classification theorem partitions all candidate universes and, more generally, all autonomous self-modeling systems satisfying the axioms into a small number of universality classes. The classification theorem applies to systems satisfying the explicit axiom package A0–A5 relative to a designated observational fragment; it is not a claim about arbitrary systems absent that structure. Applications and domain-specific consequences are treated separately as corollaries under additional premises. This overview presents the core NEMS theorem engine and selected applications; stronger domain-specific derivation and ontological synthesis claims belong to separate release surfaces with their own premise bundles and formal artifacts. The framework quantifies over arbitrary systems admitting a finite law-description and a designated observational fragment; it does not presuppose any specific physical theory, dynamics, or ontology. Trust boundary. This paper is the suite anchor for the axiom package A0–A5 and the classification theorem; machine-checked alignment is recorded in nems-lean . See .