Entropic Stabilization of Fermion Generations and Mass Hierarchy in Noncommutative Unification
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2025
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| _version_ | 1866902241527463936 |
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| author | Valeri Vukolov |
| author_facet | Valeri Vukolov |
| contents | <p>We demonstrate how the entropic stabilization of three spatial dimensions in noncommutative gravity-gauge unification naturally generates both the triplication of fermion generations and their observed mass hierarchy m1 : m2 : m3 ∼ 1 : 10^3 : 10^5. The mechanism emerges from Perelman-inspired entropy minimization constrained by topological invariants of the spatial hypersurface. Fermion masses ma<br>are shown to scale as ma ∝ exp−(a^2/2α) where a = 1, 2, 3 labels generations and α ≈ 0.90 is fixed by entropy extremization. This scaling law, rooted in the<br>anisotropic curvature coupling of the noncommutative parameter θµν, resolves the<br>generation puzzle without additional fields or fine-tuning. Testable predictions include cosmological mass evolution and modified gravitational wave spectra.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15559796 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Entropic Stabilization of Fermion Generations and Mass Hierarchy in Noncommutative Unification Valeri Vukolov noncommutative geometry, entropic stabilization, fermion generations, mass hierarchy, spatial topology, Perelman entropy, quantum gravity unification, cosmological mass evolution, Clifford algebra, geometric flow <p>We demonstrate how the entropic stabilization of three spatial dimensions in noncommutative gravity-gauge unification naturally generates both the triplication of fermion generations and their observed mass hierarchy m1 : m2 : m3 ∼ 1 : 10^3 : 10^5. The mechanism emerges from Perelman-inspired entropy minimization constrained by topological invariants of the spatial hypersurface. Fermion masses ma<br>are shown to scale as ma ∝ exp−(a^2/2α) where a = 1, 2, 3 labels generations and α ≈ 0.90 is fixed by entropy extremization. This scaling law, rooted in the<br>anisotropic curvature coupling of the noncommutative parameter θµν, resolves the<br>generation puzzle without additional fields or fine-tuning. Testable predictions include cosmological mass evolution and modified gravitational wave spectra.</p> |
| title | Entropic Stabilization of Fermion Generations and Mass Hierarchy in Noncommutative Unification |
| topic | noncommutative geometry, entropic stabilization, fermion generations, mass hierarchy, spatial topology, Perelman entropy, quantum gravity unification, cosmological mass evolution, Clifford algebra, geometric flow |
| url | https://doi.org/10.5281/zenodo.15559796 |