φ-Lattice of Elementary Particle Masses: A Precise Formula for the Muon Mass from 9 Baryon Sectors

We report the discovery of a φ-lattice structure in elementary particle masses. All 21 known baryons group into 9 sectors of the form a + b·cos(72°) with precision 10⁻¹⁶. For the muon we find the exact formula n(μ⁻) = 11 + X⁵(1 − X³/2), where n(m) = log_φ(m/m_e), X = 1/φ, with relative accuracy 5.6 × 10⁻⁷, which is three orders of magnitude better than the PDG experimental precision. All 6 known pentaquarks also fall into sectors of the same lattice. We establish exact algebraic identities relating powers of X to Fibonacci numbers through cos(72°). SU(3) structure is confirmed: octet 8/8, decuplet 10/10. The result suggests a deep connection between the golden ratio, the Fibonacci sequence, and the structure of strongly-interacting particles. Files: v50_archive.pdf, v52_publication.pdf, v53_english.pdf, v54_beamer.pdf, v56_chinese.pdf, v57_beamer_chinese.pdf.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-16
DOI
https://doi.org/10.5281/zenodo.22799461
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

φ-Lattice of Elementary Particle Masses: A Precise Formula for the Muon Mass from 9 Baryon Sectors

MOBIDUR
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

φ-Lattice of Elementary Particle Masses: A Precise Formula for the Muon Mass from 9 Baryon Sectors

MOBIDUR
preprint en

Abstract

We report the discovery of a φ-lattice structure in elementary particle masses. All 21 known baryons group into 9 sectors of the form a + b·cos(72°) with precision 10⁻¹⁶. For the muon we find the exact formula n(μ⁻) = 11 + X⁵(1 − X³/2), where n(m) = log_φ(m/m_e), X = 1/φ, with relative accuracy 5.6 × 10⁻⁷, which is three orders of magnitude better than the PDG experimental precision. All 6 known pentaquarks also fall into sectors of the same lattice. We establish exact algebraic identities relating powers of X to Fibonacci numbers through cos(72°). SU(3) structure is confirmed: octet 8/8, decuplet 10/10. The result suggests a deep connection between the golden ratio, the Fibonacci sequence, and the structure of strongly-interacting particles. Files: v50_archive.pdf, v52_publication.pdf, v53_english.pdf, v54_beamer.pdf, v56_chinese.pdf, v57_beamer_chinese.pdf.

Zenodo (CERN European Organization for Nuclear Research)
National Research Nuclear University MEPhI (RU)
Advanced Mathematical Theories and Applications
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