Сравнительный анализ SU(52), SU(56) и SU(58) в иерархии калибровочных групп
Year: 2026
Type: preprint
Abstract: This work presents a comparative analysis of three groups in the SU(n) hierarchy at k=3: SU(52), SU(56), and SU(58). Three key criteria are considered: accuracy of approximation to the fundamental constant χ/φ^5, structural interpretation, and origin from the exact polynomial. Main results: 1. SU(56) is mathematically the most accurate approximation to χ/φ^5 (deviation 0.82% vs 6.7% for SU(52) and 4.2% for SU(58)). However, SU(56) has no structural interpretation. 2. SU(58) = SU(26) × SU(32) × U(1) has a clear structural interpretation and arises from the corrected exact polynomial. 3. SU(58) is connected to string theory via 26 + 32 = 58, where 26 is the bosonic string dimension and 32 is the spinor representation of SO(32). 4. Only SU(58) gives correct physical predictions (9/9 fermion masses, RG unification, seesaw M_R). Conclusion: SU(58) is the correct choice in the gauge group hierarchy, despite SU(56) giving a more accurate mathematical approximation. Structural interpretation and physical predictions make SU(58) the only physically meaningful value. Contents:- correction_SU52_to_SU58_ru.pdf — Russian version- correction_SU52_to_SU58_en.pdf — English version- comparison_SU52_SU56_SU58_ru.pdf — Russian version- comparison_SU52_SU56_SU58_en.pdf — English version- su0_operator_SU58.py — Python implementation- su0_operator_analysis_SU58.json — Analysis results- DYNAMIC HIERARCHY GENERATION.py — Python implementation- dynamic_hierarchy_SU58.json — Results- DEGENERATE GROUP THEORY.py — Python implementation- degenerate_group_theory_SU58.json — Results License: Universal Academic Licence v1.0 (UAL-v1.0)Commercial use prohibited without author's written permission.
Author: Matershov, Sergey Viktorovich
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166308896
Cites:
Cited by:
Related to: