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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19703053 |
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| author | Bleger, Justin |
| author_facet | Bleger, Justin |
| contents | <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Derivation of the electroweak mixing angle sin²θ_W = 3/8 from the Weil representation on finite quadratic modules, without assuming SU(5) or any gauge group beyond the Standard Model. The construction begins with the Weil representation of SL₂(ℤ) on the cyclic group (ℤ/N, Q), decomposes the group algebra under parity, and computes the bilinear image of the odd-sector embedding vectors in the even subspace.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The bilinear image rank r determines the mixing angle through the trace formula sin²θ_W = r / 2(r+1). At lattice levels N = 12 and N = 84, the rank is r = 3, yielding sin²θ_W = 3/8 with charge eigenvalues {−1/3 × 3, +1, 0} — identical to the SU(5) grand unified prediction. At N = 120 (r = 6) and N = 132 (r = 5), the formula correctly predicts different values (3/7 and 5/12), providing falsification tests. All four predictions are confirmed computationally. Zero free parameters.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The derivation reproduces every entry of the SU(5) comparison table — block decomposition, tracelessness condition, eigenvalue ratio, charge spectrum, and trace ratio — from the representation theory of a finite quadratic module rather than a continuous gauge group.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">This package includes the paper (PDF, LaTeX, markdown), a Python verification script (NumPy) that independently computes all Weil matrices, embedding vectors, bilinear products, and SVD ranks at all four lattice levels, and a Lean 4 formalization providing machine-checked proofs of all integer arithmetic (42 theorems, zero sorry). A step-by-step verification guide is included for all operating systems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19703053 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | THE WEINBERG ANGLE FROM BILINEAR RANK IN THE WEIL REPRESENTATION Bleger, Justin <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Derivation of the electroweak mixing angle sin²θ_W = 3/8 from the Weil representation on finite quadratic modules, without assuming SU(5) or any gauge group beyond the Standard Model. The construction begins with the Weil representation of SL₂(ℤ) on the cyclic group (ℤ/N, Q), decomposes the group algebra under parity, and computes the bilinear image of the odd-sector embedding vectors in the even subspace.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The bilinear image rank r determines the mixing angle through the trace formula sin²θ_W = r / 2(r+1). At lattice levels N = 12 and N = 84, the rank is r = 3, yielding sin²θ_W = 3/8 with charge eigenvalues {−1/3 × 3, +1, 0} — identical to the SU(5) grand unified prediction. At N = 120 (r = 6) and N = 132 (r = 5), the formula correctly predicts different values (3/7 and 5/12), providing falsification tests. All four predictions are confirmed computationally. Zero free parameters.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The derivation reproduces every entry of the SU(5) comparison table — block decomposition, tracelessness condition, eigenvalue ratio, charge spectrum, and trace ratio — from the representation theory of a finite quadratic module rather than a continuous gauge group.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">This package includes the paper (PDF, LaTeX, markdown), a Python verification script (NumPy) that independently computes all Weil matrices, embedding vectors, bilinear products, and SVD ranks at all four lattice levels, and a Lean 4 formalization providing machine-checked proofs of all integer arithmetic (42 theorems, zero sorry). A step-by-step verification guide is included for all operating systems.</p> |
| title | THE WEINBERG ANGLE FROM BILINEAR RANK IN THE WEIL REPRESENTATION |
| url | https://doi.org/10.5281/zenodo.19703053 |