{"paper":{"title":"Fermion mass ratios from the exceptional Jordan algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Tejinder P. Singh","submitted_at":"2025-08-13T18:53:19Z","abstract_excerpt":"The origin of the three fermion generations and their highly hierarchical mass spectra remains one of the most profound puzzles in particle physics. We show that the complexified exceptional Jordan algebra $J_{3}(\\mathbb{O}_{\\mathbb{C}})$, the natural mathematical framework for the exceptional Lie group $E_{6}$, provides a unified explanation for both. The three generations arise from the three off-diagonal Peirce slots of $J_{3}(\\mathbb{O}_{\\mathbb{C}})$, each carrying an isomorphic $Cl(6,\\mathbb C)$ minimal-ideal fiber and permuted cyclically by triality $S_3\\subset\\mathrm{Out}(\\mathrm{Spin}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.10131","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.10131/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}