{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PRTPESUQHSCLP27CVVLP4YUTJQ","short_pith_number":"pith:PRTPESUQ","schema_version":"1.0","canonical_sha256":"7c66f24a903c84b7ebe2ad56fe62934c0b9a7056b43bdb43cb39116497f2a76e","source":{"kind":"arxiv","id":"2412.19691","version":2},"attestation_state":"computed","paper":{"title":"Quantum Many-Body Lattice C-R-T Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Juven Wang, Yang-Yang Li, Yi-Zhuang You","submitted_at":"2024-12-27T15:36:31Z","abstract_excerpt":"Charge conjugation (C), mirror reflection (R), and time reversal (T) symmetries, along with internal symmetries, are essential for massless Majorana and Dirac fermions. These symmetries are sufficient to rule out potential fermion bilinear mass terms, thereby establishing a gapless free fermion fixed point phase, pivotal for symmetric mass generation (SMG) transition. In this work, we systematically study the anomaly of C-R-T-internal symmetry in all spacetime dimensions by analyzing the projective representation (i.e. the fractionalization) of the C-R-T-internal symmetry group in the quantum "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.19691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-12-27T15:36:31Z","cross_cats_sorted":["hep-lat","hep-th","quant-ph"],"title_canon_sha256":"751cbdf3b2aa07f26b0c89b703689dd3d38fdb8c02acbf788abe6d90c3ef5f9b","abstract_canon_sha256":"112915313d977bb86cb7bbdf0c2b0505f2e6582b79f8964d3606d39064748af0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:57.307985Z","signature_b64":"CHnKPSoAUKc+9al9F+PxbC0HFH1LR8DxZ0xbjx19mEj/Yp4IRB2adYFrqLnnn1g+PTkcJl6zA7v4+bj8yrzyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c66f24a903c84b7ebe2ad56fe62934c0b9a7056b43bdb43cb39116497f2a76e","last_reissued_at":"2026-07-05T12:07:57.307443Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:57.307443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Many-Body Lattice C-R-T Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Juven Wang, Yang-Yang Li, Yi-Zhuang You","submitted_at":"2024-12-27T15:36:31Z","abstract_excerpt":"Charge conjugation (C), mirror reflection (R), and time reversal (T) symmetries, along with internal symmetries, are essential for massless Majorana and Dirac fermions. These symmetries are sufficient to rule out potential fermion bilinear mass terms, thereby establishing a gapless free fermion fixed point phase, pivotal for symmetric mass generation (SMG) transition. In this work, we systematically study the anomaly of C-R-T-internal symmetry in all spacetime dimensions by analyzing the projective representation (i.e. the fractionalization) of the C-R-T-internal symmetry group in the quantum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19691","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/2412.19691/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.19691","created_at":"2026-07-05T12:07:57.307503+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.19691v2","created_at":"2026-07-05T12:07:57.307503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19691","created_at":"2026-07-05T12:07:57.307503+00:00"},{"alias_kind":"pith_short_12","alias_value":"PRTPESUQHSCL","created_at":"2026-07-05T12:07:57.307503+00:00"},{"alias_kind":"pith_short_16","alias_value":"PRTPESUQHSCLP27C","created_at":"2026-07-05T12:07:57.307503+00:00"},{"alias_kind":"pith_short_8","alias_value":"PRTPESUQ","created_at":"2026-07-05T12:07:57.307503+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.06022","citing_title":"Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions","ref_index":64,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06022","citing_title":"Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions","ref_index":64,"is_internal_anchor":false},{"citing_arxiv_id":"2604.02078","citing_title":"Taste-splitting mass and edge modes in $3+1$ D staggered fermions","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06022","citing_title":"Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions","ref_index":62,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06307","citing_title":"Lattice chiral symmetry from bosons in 3+1d","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ","json":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ.json","graph_json":"https://pith.science/api/pith-number/PRTPESUQHSCLP27CVVLP4YUTJQ/graph.json","events_json":"https://pith.science/api/pith-number/PRTPESUQHSCLP27CVVLP4YUTJQ/events.json","paper":"https://pith.science/paper/PRTPESUQ"},"agent_actions":{"view_html":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ","download_json":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ.json","view_paper":"https://pith.science/paper/PRTPESUQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.19691&json=true","fetch_graph":"https://pith.science/api/pith-number/PRTPESUQHSCLP27CVVLP4YUTJQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PRTPESUQHSCLP27CVVLP4YUTJQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ/action/storage_attestation","attest_author":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ/action/author_attestation","sign_citation":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ/action/citation_signature","submit_replication":"https://pith.science/pith/PRTPESUQHSCLP27CVVLP4YUTJQ/action/replication_record"}},"created_at":"2026-07-05T12:07:57.307503+00:00","updated_at":"2026-07-05T12:07:57.307503+00:00"}