Instantiating No External Model Selection in Physics Macroscopic Records, Non-Categoricity, and a Criterion for Class IIb
Year: 2026
Type: preprint
Abstract: We instantiate the No External Model Selection Theorem in a physics-grounded setting by fixing an observational fragment based on stable macroscopic records. Building on the universality-class classification of realized systems under single actuality, no external model selection, and no free completion bits, we provide explicit sufficient conditions under which a realized universe must lie in Class IIb relative to the record language: observational multiplicity forces internal selection, and diagonal-capable self-reference on the same record fragment forbids total effective selection. The paper contributes (i) a minimal, operational definition of a record language \LangRec and its record-truth semantics; (ii) a minimality theorem showing that \LangRec captures the weakest standard observational commitments needed for empirical science; (iii) two complementary routes to establishing record-level non-categoricity in physically universal systems; and (iv) a theorem package separating a core Class IIb criterion from domain-specific premises that imply its hypotheses. The result is a conditional but sharp classification statement about the semantic architecture required of any closed, definite, computationally universal physical world. Trust boundary. Class IIb claims are conditional on the record-language and computability premises of this paper; the classification engine itself is in Paper 2, with formal companions in nems-lean . See .
Author: Spivack, Nova
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7149955009
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