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JCGM 101:2008 (2008) Evaluation of Measurement Data-Supplement 1: Propagation of Distributions Using a Monte Carlo Method. Joint Committee for Guides in Metrology.

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• TITLE: Beyond Gödel: Information-Theoretical Limits of Physical Models and the Principle of Optimal Incompleteness

  AUTHORS: Boris Menin

  KEYWORDS: Information Theory, Model Uncertainty, Physical Constants, Gödel’s Incompleteness, Comparative Uncertainty, Measurement Limits, Phenomenological Group, Optimal Modeling, Metrology

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.1, January 5, 2026

  ABSTRACT: A new conceptual framework is presented that unifies Gödel’s incompleteness theorems with practical physical modeling through information-theoretic analysis. The method of variables with finite information content demonstrates that every physical model inherits an irreducible uncertainty, representing a “Gödelian barrier” in physics. Models with too few variables are incomplete and yield high uncertainty, while models with an excessive number of variables become computationally intractable despite theoretical completeness. The concept is validated by a systematic analysis of measurements of six fundamental constants across sixty-five scientific publications from the period 2000-2019. The method provides quantitative criteria for model selection, explains systematic discrepancies in precision measurements, and establishes fundamental limits to measurement accuracy independent of improvements in instrumental technology. This work offers researchers a practical tool for assessing model adequacy and understanding why certain physical constants resist precise determination.