Lepton Mass Ratios from Near-Critical Spectral Collapse on a Kaluza-Klein Lattice
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Veröffentlicht: |
Zenodo
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901802457235456 |
|---|---|
| author | Strech, Nathan |
| author_facet | Strech, Nathan |
| contents | <p><em>1st installment of the N=8 Kaluza–Klein cycle graph series (Preprints 1–15).<br></em></p> <p><br>This paper presents a spectral-geometry mechanism for the charged-lepton mass hierarchy based on a KK-weighted N=8 cycle graph with a localized defect and near-critical spectral collapse.</p> <p>Key results:</p> <ul> <li>Demonstrates a P/Q sector mechanism (via Löwdin/Feshbach–Schur reduction) in which the electron emerges as a near-critical survivor while μ and τ arise as dressed KK tower modes.</li> <li>Proves a rank-3 minimum theorem for the defect structure.</li> <li>Shows the Koide residual varies monotonically along the near-critical family and can be used as a selection constraint for the physical point.</li> <li>A scan over lattice sizes N=6–24 (even and odd) shows that N=8 is the unique value admitting an endpoint Koide crossing, providing a spectral selection principle for the lattice size.</li> <li>Yields a prediction for m_τ that provides a high-precision consistency check accessible to Belle II (~2027).</li> </ul> <p>Reproducibility materials (LaTeX source, figures, and a reference Python implementation) are provided in the attached ZIP.<br><br></p> <p><em>Companion preprints in this series:</em></p> <p><em>1. (10.5281/zenodo.18901940) Lepton Mass Ratios from Near-Critical Spectral Collapse on a KK Lattice</em><br><em>2. (10.5281/zenodo.19069130) Quark and Neutrino Masses, Mixing, and CP Violation from Spectral Collapse on a KK Lattice</em><br><em>3. (10.5281/zenodo.19102395) Derivation of Flavor-Mixing Operators from Spectral Healing on a KK Lattice</em><br><em>4. (10.5281/zenodo.19138814) A Dimensional Signature in Fermion Mass Ratios on a KK Lattice</em><br><em>5. (10.5281/zenodo.19164984) Quadratic Warping and the ∆n=2 Selection Rule on an N=8 KK Lattice</em><br><em>6. (10.5281/zenodo.19197437) Spectral Singularity Selectors for Charged-Flavor Defect Parameters on an N=8 KK Lattice</em><br><em>7. (10.5281/zenodo.19333892) Scalar Fluctuations and the Gap-Protected Common Mass Space of the Warped N=8 KK Lattice</em><br><em>8. (10.5281/zenodo.19402377) Electroweak structure, gravity, and the Standard Model gauge group from a warped eight-site KK lattice</em><br><em>9. (10.5281/zenodo.19499071) Cross-port tunneling and spectral normalization on the warped N=8 KK lattice</em><br><em>10. (10.5281/zenodo.19513847) Universal sector readout, fermion mixing, and strong CP from the N=8 warped cycle graph</em><br><em>11. (10.5281/zenodo.19554696) The color-gateway threshold and strong coupling from the N=8 warped cycle graph</em><br><em>12. (10.5281/zenodo.19653058) PMNS operator anatomy from bridge-local Feshbach reduction on the N=8 warped cycle graph</em><br><em>13. (10.5281/zenodo.19665262) Rank-one bridge operator, bipartite-grading breaking, and Higgs-sector response on the N=8 warped cycle graph</em><br><em>14. (10.5281/zenodo.19683382) KK Lagrangian, overlap tensors, and low-mode Feynman rules on the N=8 warped cycle graph</em><br><em>15. (10.5281/zenodo.19949517) A paired zero-mode mechanism for the cosmological constant on the N=8 warped cycle graph</em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19138470 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Lepton Mass Ratios from Near-Critical Spectral Collapse on a Kaluza-Klein Lattice Strech, Nathan Löwdin reduction Standard Model Flavor Physics Lepton Masses Koide Relation Koide Formula Spectral Geometry Graph Theory Kaluza-Klein Theory Discrete Laplacians Feshbach-Schur Reduction Spectral Collapse Near-Criticality Gaussian Defect Eigenvalue Spectrum <p><em>1st installment of the N=8 Kaluza–Klein cycle graph series (Preprints 1–15).<br></em></p> <p><br>This paper presents a spectral-geometry mechanism for the charged-lepton mass hierarchy based on a KK-weighted N=8 cycle graph with a localized defect and near-critical spectral collapse.</p> <p>Key results:</p> <ul> <li>Demonstrates a P/Q sector mechanism (via Löwdin/Feshbach–Schur reduction) in which the electron emerges as a near-critical survivor while μ and τ arise as dressed KK tower modes.</li> <li>Proves a rank-3 minimum theorem for the defect structure.</li> <li>Shows the Koide residual varies monotonically along the near-critical family and can be used as a selection constraint for the physical point.</li> <li>A scan over lattice sizes N=6–24 (even and odd) shows that N=8 is the unique value admitting an endpoint Koide crossing, providing a spectral selection principle for the lattice size.</li> <li>Yields a prediction for m_τ that provides a high-precision consistency check accessible to Belle II (~2027).</li> </ul> <p>Reproducibility materials (LaTeX source, figures, and a reference Python implementation) are provided in the attached ZIP.<br><br></p> <p><em>Companion preprints in this series:</em></p> <p><em>1. (10.5281/zenodo.18901940) Lepton Mass Ratios from Near-Critical Spectral Collapse on a KK Lattice</em><br><em>2. (10.5281/zenodo.19069130) Quark and Neutrino Masses, Mixing, and CP Violation from Spectral Collapse on a KK Lattice</em><br><em>3. (10.5281/zenodo.19102395) Derivation of Flavor-Mixing Operators from Spectral Healing on a KK Lattice</em><br><em>4. (10.5281/zenodo.19138814) A Dimensional Signature in Fermion Mass Ratios on a KK Lattice</em><br><em>5. (10.5281/zenodo.19164984) Quadratic Warping and the ∆n=2 Selection Rule on an N=8 KK Lattice</em><br><em>6. (10.5281/zenodo.19197437) Spectral Singularity Selectors for Charged-Flavor Defect Parameters on an N=8 KK Lattice</em><br><em>7. (10.5281/zenodo.19333892) Scalar Fluctuations and the Gap-Protected Common Mass Space of the Warped N=8 KK Lattice</em><br><em>8. (10.5281/zenodo.19402377) Electroweak structure, gravity, and the Standard Model gauge group from a warped eight-site KK lattice</em><br><em>9. (10.5281/zenodo.19499071) Cross-port tunneling and spectral normalization on the warped N=8 KK lattice</em><br><em>10. (10.5281/zenodo.19513847) Universal sector readout, fermion mixing, and strong CP from the N=8 warped cycle graph</em><br><em>11. (10.5281/zenodo.19554696) The color-gateway threshold and strong coupling from the N=8 warped cycle graph</em><br><em>12. (10.5281/zenodo.19653058) PMNS operator anatomy from bridge-local Feshbach reduction on the N=8 warped cycle graph</em><br><em>13. (10.5281/zenodo.19665262) Rank-one bridge operator, bipartite-grading breaking, and Higgs-sector response on the N=8 warped cycle graph</em><br><em>14. (10.5281/zenodo.19683382) KK Lagrangian, overlap tensors, and low-mode Feynman rules on the N=8 warped cycle graph</em><br><em>15. (10.5281/zenodo.19949517) A paired zero-mode mechanism for the cosmological constant on the N=8 warped cycle graph</em></p> |
| title | Lepton Mass Ratios from Near-Critical Spectral Collapse on a Kaluza-Klein Lattice |
| topic | Löwdin reduction Standard Model Flavor Physics Lepton Masses Koide Relation Koide Formula Spectral Geometry Graph Theory Kaluza-Klein Theory Discrete Laplacians Feshbach-Schur Reduction Spectral Collapse Near-Criticality Gaussian Defect Eigenvalue Spectrum |
| url | https://doi.org/10.5281/zenodo.19138470 |