{"paper":{"title":"C-R-T Fractionalization, Fermions, and Mod 8 Periodicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Juven Wang, Shing-Tung Yau, Yi-Zhuang You, Zheyan Wan","submitted_at":"2023-12-28T17:04:36Z","abstract_excerpt":"Charge conjugation (C), mirror reflection (R), time reversal (T), and fermion parity $(-1)^{\\rm F}$ are basic discrete spacetime and internal symmetries of the Dirac fermions. In this article, we determine the group, called the C-R-T fractionalization, which is a group extension of $\\mathbb{Z}_2^{\\rm C}\\times\\mathbb{Z}_2^{\\rm R}\\times\\mathbb{Z}_2^{\\rm T}$ by the fermion parity $\\mathbb{Z}_2^{\\rm F}$, and its extension class in all spacetime dimensions $d$, for a single-particle fermion theory. For Dirac fermions, with the canonical CRT symmetry $\\mathbb{Z}_2^{\\rm CRT}$, the C-R-T fractionaliza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.17126","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/2312.17126/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"}