9 - Anisotropic Constitutive Closure of the Charged-Lepton Hierarchy from a Bi-Scale Topological Defect
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2026
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| _version_ | 1866901795013394432 |
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| author | Jublot, Thomas |
| author_facet | Jublot, Thomas |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20316150 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | 9 - Anisotropic Constitutive Closure of the Charged-Lepton Hierarchy from a Bi-Scale Topological Defect Jublot, Thomas constitutive anisotropy anisotropic Hessian charged-lepton hierarchy muon–electron ratio tau collective excitation core–halo topology anisotropic effective medium spectral mass hierarchy topological lepton defect collective locking sector constitutive kernel phase-rigidity theory <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> |
| title | 9 - Anisotropic Constitutive Closure of the Charged-Lepton Hierarchy from a Bi-Scale Topological Defect |
| topic | constitutive anisotropy anisotropic Hessian charged-lepton hierarchy muon–electron ratio tau collective excitation core–halo topology anisotropic effective medium spectral mass hierarchy topological lepton defect collective locking sector constitutive kernel phase-rigidity theory |
| url | https://doi.org/10.5281/zenodo.20316150 |