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April 2026

The σ² Theorem

σ² = 0.381966… is the universal eigenvalue of self-reference in physics. Standard Model parameters are addresses in a finite directory of σ representations, not independent values. Nine worked examples across fifteen physical sectors, with four experimental falsification thresholds.

Eric McLean · Independent Researcher, Edinburgh · Pentagon Physics · 30 April 2026 · DOI
9Worked examples
15Physical sectors
4Falsification thresholds
0Free parameters
Key Results

One eigenvalue across fifteen sectors

This paper proposes σ² = 0.381966… as the universal eigenvalue of self-reference in physics. It argues that Standard Model parameters represent addresses in a finite directory of σ representations rather than independent values. The work presents a theorem claiming that in self-referential systems, relaxation rates, partition coefficients, and consistency operator eigenvalues equal σ². Nine worked examples across fifteen physical sectors are provided, and four experimental thresholds are identified that could falsify the framework within three to ten years.

↗ Read on Zenodo doi:10.5281/zenodo.19917820