{"paper":{"title":"Three Generations and a Trio of Trialities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"M.J. Hughes, N. Furey","submitted_at":"2024-09-26T15:22:10Z","abstract_excerpt":"We identify the Standard Model's $\\mathfrak{su}(3)\\oplus \\mathfrak{su}(2)\\oplus \\mathfrak{u}(1)$ internal symmetries within the triality symmetries $\\mathfrak{tri}(\\mathbb{C}) \\oplus \\mathfrak{tri}(\\mathbb{H}) \\oplus \\mathfrak{tri}(\\mathbb{O})$. From here, the corresponding Standard Model group action is applied to the triality triple $\\left( \\Psi_+, \\Psi_-,V\\right)$ for $\\Psi_+, \\Psi_-, V \\in \\mathbb{C}\\otimes\\mathbb{H}\\otimes\\mathbb{O}$. Together, $\\Psi_+$ and $\\Psi_-$ provide the correct irreducible representations for two generations. Owing to a certain Cartan Factorization, which we defin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17948","kind":"arxiv","version":2},"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/2409.17948/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"}