Paper CIV: Chapter P The CKM Hierarchy from G2 Lattice Edge Topology Lattice Edges on Non-Root Nodes; G2 Short/Long Root Classication; Gen3 H−Penalty:
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| Lingua: | inglese |
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2026
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| _version_ | 1866901494682353664 |
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| author | Jagadeesan, Bharathi Dasan |
| author_facet | Jagadeesan, Bharathi Dasan |
| contents | <p>The hop counting framework of Paper CII (which counts only Fano-collinear transitions) fails to distinguish |Vus| ≈λ from |Vcb| ≈λ2, since both are one Fano- adjacency step. Bharathi (2026) identies the resolution: in the physical G2 Fano spacetime lattice, hops are also possible at lattice edges between nodes not connected by a single G2 root step. The G2 root system classies connections as: short roots (within H+ or within H−, amplitude ∼λ), long roots (any node to e7, amplitude ∼1), and non-root composite lattice edges (H+ ↔H−cross-sector, requiring two G2 root steps, amplitude ∼λ2 or requiring an extra factor of λ). The H+/H−composition of each generation line is: Gen 1 (u, d): 2 3H+, Gen 2 (c, s): 1 3H+, Gen 3 (t, b): 0 · H+ (entirely H−). The complete rule is: nhops = |generation gap| + δGen3 where δGen3 = 1 if Gen 3 is involved in the transition (as source or target) and 0 oth- erwise. The CKM amplitude |Vij| ≈λnhops. This single rule predicts all nine CKM elements: |Vus|, |Vcd| ≈λ (to 0.1%); |Vcb|, |Vts| ≈λ2 with A = |Vcb|/λ2 = 0.827 (ob- served APDG = 0.811, agreement 2%); |Vub|, |Vtd| ≈λ3×(complex phase factor). The Wolfenstein parameter A emerges from the Gen3 H−penalty without any additional input. Four new predictions are made (P76P79).</p><p><em>Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: <a href="https://doi.org/10.5281/zenodo.19120873">10.5281/zenodo.19120873</a>. Community: <strong>one-octonion-brane-bulk</strong>. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.</em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20300084 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Paper CIV: Chapter P The CKM Hierarchy from G2 Lattice Edge Topology Lattice Edges on Non-Root Nodes; G2 Short/Long Root Classication; Gen3 H−Penalty: Jagadeesan, Bharathi Dasan One-Octonion Brane-Bulk Framework G2 octonion Klein quartic Fano plane auxetic brane <p>The hop counting framework of Paper CII (which counts only Fano-collinear transitions) fails to distinguish |Vus| ≈λ from |Vcb| ≈λ2, since both are one Fano- adjacency step. Bharathi (2026) identies the resolution: in the physical G2 Fano spacetime lattice, hops are also possible at lattice edges between nodes not connected by a single G2 root step. The G2 root system classies connections as: short roots (within H+ or within H−, amplitude ∼λ), long roots (any node to e7, amplitude ∼1), and non-root composite lattice edges (H+ ↔H−cross-sector, requiring two G2 root steps, amplitude ∼λ2 or requiring an extra factor of λ). The H+/H−composition of each generation line is: Gen 1 (u, d): 2 3H+, Gen 2 (c, s): 1 3H+, Gen 3 (t, b): 0 · H+ (entirely H−). The complete rule is: nhops = |generation gap| + δGen3 where δGen3 = 1 if Gen 3 is involved in the transition (as source or target) and 0 oth- erwise. The CKM amplitude |Vij| ≈λnhops. This single rule predicts all nine CKM elements: |Vus|, |Vcd| ≈λ (to 0.1%); |Vcb|, |Vts| ≈λ2 with A = |Vcb|/λ2 = 0.827 (ob- served APDG = 0.811, agreement 2%); |Vub|, |Vtd| ≈λ3×(complex phase factor). The Wolfenstein parameter A emerges from the Gen3 H−penalty without any additional input. Four new predictions are made (P76P79).</p><p><em>Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: <a href="https://doi.org/10.5281/zenodo.19120873">10.5281/zenodo.19120873</a>. Community: <strong>one-octonion-brane-bulk</strong>. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.</em></p> |
| title | Paper CIV: Chapter P The CKM Hierarchy from G2 Lattice Edge Topology Lattice Edges on Non-Root Nodes; G2 Short/Long Root Classication; Gen3 H−Penalty: |
| topic | One-Octonion Brane-Bulk Framework G2 octonion Klein quartic Fano plane auxetic brane |
| url | https://doi.org/10.5281/zenodo.20300084 |