保存先:
| 第一著者: | |
|---|---|
| フォーマット: | Recurso digital |
| 言語: | |
| 出版事項: |
Zenodo
2026
|
| 主題: | |
| オンライン･アクセス: | https://doi.org/10.5281/zenodo.19064152 |
| タグ: |
タグ追加
タグなし, このレコードへの初めてのタグを付けませんか!
|
目次:
- <p>We derive the colour gauge algebra <span><span><span><span><span><span>su</span></span><span>(</span><span>3</span><span>)</span></span></span></span></span> and the leading-order magnetic moment ratio <span><span><span><span><span><span>μ</span><span><span><span><span><span><span><span>n</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span>μ</span><span><span><span><span><span><span><span>p</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>−</span><span>2/3</span></span></span></span></span> from the topology of the trefoil knot <span><span><span><span><span>T</span><span>(</span><span>2</span><span>,</span><span>3</span><span>)</span></span></span></span></span> within the Discrete Topological Torsion Theory (DTTT) framework, and propose a topological mechanism for exactly three fermion generations and colour confinement. The derivation of <span><span><span><span><span><span>su</span></span><span>(</span><span>3</span><span>)</span></span></span></span></span> proceeds through a four-step chain of established theorems: Fox 3-colouring <span><span><span><span><span>→</span></span><span><span><span>S</span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span></span><span>→</span></span><span><span><span>A</span><span><span><span><span><span><span><span>2</span></span></span></span><span></span></span></span></span></span></span></span></span></span> root lattice (Proposition 5.1) <span><span><span><span><span>→</span></span><span><span><span>su</span></span><span>(</span><span>3</span><span>)</span></span></span></span></span> via Serre's theorem. The three-generation structure follows from the Milnor fibre genus formula <span><span><span><span><span>g</span><span>(</span><span>T</span><span>(</span><span>2</span><span>,</span><span>q</span><span>))</span><span>=</span></span><span><span>(</span><span>q</span><span>−</span></span><span><span>1</span><span>)</span><span>/2</span></span></span></span></span> combined with a topological stability bound; the Callias index computation that would complete this argument is precisely stated as an open problem (Conjecture 6.2). The sign of <span><span><span><span><span><span>m</span><span><span><span><span><span><span><span>n</span></span></span></span><span></span></span></span></span></span><span>></span></span><span><span><span>m</span><span><span><span><span><span><span><span>p</span></span></span></span><span></span></span></span></span></span></span></span></span></span> is derived from inter-lobe Coulomb sums with zero free parameters. All results operate within <span><span><span><span><span>3</span><span>+</span></span><span><span>1</span></span></span></span></span> dimensions; extra dimensions are excluded by the Poplawski theorem. Three problems - the absolute W-boson mass, the Yukawa hierarchy, and the exact path-integral derivation of <span><span><span><span><span><span>n</span><span><span><span><span><span><span><span>T</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>4</span></span></span></span></span> - remain irreducibly open and are stated as such.</p>