{"paper":{"title":"Standard Model Symmetries and the Nested Embeddings of $\\mathbb{R}\\subset\\mathbb{C}\\subset\\mathbb{H}\\subset\\mathbb{O}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"N. Furey","submitted_at":"2026-07-20T19:00:48Z","abstract_excerpt":"Where do the Standard Model's internal symmetries come from? Treating $\\mathbb{O}\\oplus\\mathbb{H}\\oplus\\mathbb{C}\\oplus\\mathbb{R}$ as a module for its own multiplication algebra enables a particular origin story for the Standard Model's pre-Higgs, $\\mathfrak{g}_{SM}:=\\mathfrak{su}(3)_{C} \\oplus \\mathfrak{su}(2)_{L} \\oplus \\mathfrak{u}(1)_{Y},$ and post-Higgs, $\\mathfrak{g}_{LE}:=\\mathfrak{su}(3)_{C} \\oplus \\mathfrak{u}(1)_{Q},$ symmetries. We recognize both these endomorphisms and their modules alike as $\\mathbb{Z}_2^n$-graded algebras. Then, annihilating certain highest grade (volume) element"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18450","kind":"arxiv","version":1},"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/2607.18450/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"}