{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:RBYUTQORSPKA3LPQINJEQ5WPVN","short_pith_number":"pith:RBYUTQOR","schema_version":"1.0","canonical_sha256":"887149c1d193d40dadf043524876cfab5e4c2dfdfa41dbc854b2619ea0e49b5c","source":{"kind":"arxiv","id":"2007.00575","version":3},"attestation_state":"computed","paper":{"title":"$\\mathbb{Z}_2$-projective translational symmetry protected topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Shengyuan A. Yang, Yue-Xin Huang, Y. X. Zhao","submitted_at":"2020-07-01T16:02:54Z","abstract_excerpt":"Symmetry is fundamental to topological phases. In the presence of a gauge field, spatial symmetries will be projectively represented, which may alter their algebraic structure and generate novel topological phases. We show that the $\\mathbb{Z}_2$ projectively represented translational symmetry operators adopt a distinct commutation relation, and become momentum dependent analogous to twofold nonsymmorphic symmetries. Combined with other internal or external symmetries, they give rise to many exotic band topology, such as the degeneracy over the whole boundary of the Brillouin zone, the single "},"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":"2007.00575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-07-01T16:02:54Z","cross_cats_sorted":["cond-mat.str-el","quant-ph"],"title_canon_sha256":"5822a8db7d6f0588304a75117ac52ebe77492378721abd05a8be0dacd22d67ee","abstract_canon_sha256":"4480251a6d311307cf8f7da0293340a7e225158e45f31fb0c8efb65f057cdc07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:48:48.213692Z","signature_b64":"uPM8zTAz/qyc6ZjiazB8O3nwDZm2/HWnTQRlWJiBPx8j5HOCbKdifTbG9YkWO5m6dGQ+9PckDCcYniNWA0G1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"887149c1d193d40dadf043524876cfab5e4c2dfdfa41dbc854b2619ea0e49b5c","last_reissued_at":"2026-07-05T01:48:48.213273Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:48:48.213273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathbb{Z}_2$-projective translational symmetry protected topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Shengyuan A. Yang, Yue-Xin Huang, Y. X. Zhao","submitted_at":"2020-07-01T16:02:54Z","abstract_excerpt":"Symmetry is fundamental to topological phases. In the presence of a gauge field, spatial symmetries will be projectively represented, which may alter their algebraic structure and generate novel topological phases. We show that the $\\mathbb{Z}_2$ projectively represented translational symmetry operators adopt a distinct commutation relation, and become momentum dependent analogous to twofold nonsymmorphic symmetries. Combined with other internal or external symmetries, they give rise to many exotic band topology, such as the degeneracy over the whole boundary of the Brillouin zone, the single "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.00575","kind":"arxiv","version":3},"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/2007.00575/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":"2007.00575","created_at":"2026-07-05T01:48:48.213336+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.00575v3","created_at":"2026-07-05T01:48:48.213336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.00575","created_at":"2026-07-05T01:48:48.213336+00:00"},{"alias_kind":"pith_short_12","alias_value":"RBYUTQORSPKA","created_at":"2026-07-05T01:48:48.213336+00:00"},{"alias_kind":"pith_short_16","alias_value":"RBYUTQORSPKA3LPQ","created_at":"2026-07-05T01:48:48.213336+00:00"},{"alias_kind":"pith_short_8","alias_value":"RBYUTQOR","created_at":"2026-07-05T01:48:48.213336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN","json":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN.json","graph_json":"https://pith.science/api/pith-number/RBYUTQORSPKA3LPQINJEQ5WPVN/graph.json","events_json":"https://pith.science/api/pith-number/RBYUTQORSPKA3LPQINJEQ5WPVN/events.json","paper":"https://pith.science/paper/RBYUTQOR"},"agent_actions":{"view_html":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN","download_json":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN.json","view_paper":"https://pith.science/paper/RBYUTQOR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.00575&json=true","fetch_graph":"https://pith.science/api/pith-number/RBYUTQORSPKA3LPQINJEQ5WPVN/graph.json","fetch_events":"https://pith.science/api/pith-number/RBYUTQORSPKA3LPQINJEQ5WPVN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN/action/storage_attestation","attest_author":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN/action/author_attestation","sign_citation":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN/action/citation_signature","submit_replication":"https://pith.science/pith/RBYUTQORSPKA3LPQINJEQ5WPVN/action/replication_record"}},"created_at":"2026-07-05T01:48:48.213336+00:00","updated_at":"2026-07-05T01:48:48.213336+00:00"}