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| Үндсэн зохиолч: | |
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| Формат: | Recurso digital |
| Хэл сонгох: | |
| Хэвлэсэн: |
Zenodo
2026
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| Нөхцлүүд: | |
| Онлайн хандалт: | https://doi.org/10.5281/zenodo.20316150 |
| Шошгууд: |
Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
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Агуулга:
- <p>We construct an anisotropic constitutive closure of the charged-lepton hierarchy within the bi-scale topological defect framework of the phase–rigidity programme. The effective medium is described by the constitutive tensor</p> <p>\[<br>C^{ij}(r)<br>=<br>c_r^2(r)\hat r^i\hat r^j<br>+<br>c_\perp^2(r)<br>\left(<br>\delta^{ij}-\hat r^i\hat r^j<br>\right),<br>\]</p> <p>with reduced anisotropy parameter</p> <p>\[<br>Y=\frac{c_c}{c_s}.<br>\]</p> <p>The constitutive-topological kernel becomes</p> <p>\[<br>W_Y(r)<br>=<br>\frac{4+8/Y}{(1+r^2)^3}.<br>\]</p> <p>The reduced anisotropic Hessian admits a unique localized</p> <p>\[<br>K=0<br>\]</p> <p>bound state with eigenvalue</p> <p>\[<br>q_c\simeq2.2767,<br>\qquad<br>Y=\sqrt{q_c}\simeq1.5089,<br>\]</p> <p>yielding the effective muonic relation</p> <p>\[<br>\frac{m_\mu}{m_e}<br>=<br>\alpha^{-1}\sqrt{q_c}<br>\simeq206.77.<br>\]</p> <p>The minimal local</p> <p>\[<br>K=1<br>\]</p> <p>sector remains above threshold and does not produce a localized tau mode. The tau sector is instead interpreted as a finite collective torsional excitation of the same defect,</p> <p>\[<br>\vartheta(t)=\theta_c(t)-\theta_h(t),<br>\]</p> <p>with collective frequency</p> <p>\[<br>\omega_\tau^2\simeq2.06.<br>\]</p> <p>This gives the effective tau hierarchy</p> <p>\[<br>\frac{m_\tau}{m_\mu}<br>=<br>\sqrt{1+\alpha^{-1}\omega_\tau^2}<br>\simeq16.82.<br>\]</p> <p>The same anisotropic constitutive kernel therefore controls the localized muonic mode, the collective tau sector, and the stationary core–halo interface structure. The framework remains explicitly effective and phenomenological rather than UV-complete.</p>