The Diagonalization Barrier: Universal Self-Reference and Structural Asymmetry — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-16
DOI
https://doi.org/10.5281/zenodo.22786477
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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preprint

The Diagonalization Barrier: Universal Self-Reference and Structural Asymmetry — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

The Diagonalization Barrier: Universal Self-Reference and Structural Asymmetry — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Diagonalization is the core fixed-point-free involution underlying Gödelian incompleteness, Turing undecidability, and spontaneous symmetry breaking in quantum systems — a universal "self-reference barrier" that generates structural asymmetry from symmetric formal systems. | MATH: The diagonal argument constructs a fixed-point-free map \( f: X \to X \) with \( f(x) \neq x \) for all \( x \) (e.g., Cantor's \( d(n) = 1 - a_{nn} \)). In computability, this yields the halting problem's undecidability via the self-referential program \( P \) that halts iff it doesn't. Gödel's fixed-point lemma: for any formula \( \phi(x) \), there exists a sentence \( \psi \) with \( \psi \leftrightarrow \phi(\ulcorner \psi \urcorner) \). The Wigner-Eckart corrections paper (arXiv:2007.03539) shows spontaneous symmetry breaking \( G \to H \) modifies matrix elements by corrections proportional to \( \langle \phi | \hat{O} | \psi \rangle = \sum_\lambda C^\lambda \langle j_1 m_1; \lambda \mu | j_2 m Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
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