{"paper":{"title":"The Dirac equation in (split-)octonions: origins, variants, and modern context","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.RA"],"primary_cat":"math-ph","authors_text":"J. K\\\"oplinger","submitted_at":"2026-06-21T22:01:23Z","abstract_excerpt":"Octonions and split-octonions have been used to express the Dirac equation in physics in several conceptually distinct ways. This review sorts them into four groups: the 2-factor (direct-product), 3-factor, and projection representations, which use (split-)octonion basis elements natively to model a spacetime basis; and the conventional use of octonions to carry Dirac algebra acting on spinors. Pointers to their modern use, and to recent methods for native split-octonionic analysis, are given throughout. Within the 2-factor approach, we document its origin (J. K\\\"oplinger, Appl. Math. Computat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09703","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/2607.09703/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"}