{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:WRBF5A333YP7EMVG2WFQWUCSB6","short_pith_number":"pith:WRBF5A33","schema_version":"1.0","canonical_sha256":"b4425e837bde1ff232a6d58b0b50520fa04cf69cb92ce1e762b9cfd37a0a489d","source":{"kind":"arxiv","id":"2403.18573","version":1},"attestation_state":"computed","paper":{"title":"Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andras Molnar, Jose Garre Rubio, Yoshiko Ogata","submitted_at":"2024-03-27T13:54:45Z","abstract_excerpt":"We consider the classification problem of quantum spin chains invariant under local decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated to them. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological (SPT) phases. We prove that these invariants coincide with the ones of [J. Garre Rubio et al, Q"},"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":"2403.18573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-03-27T13:54:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ef19f77e00b22b1336b0b3b85c3e77eeedc521bc0decc38a7c3875d42bfc9ca3","abstract_canon_sha256":"df7e2ad5e4d72cdea07dee4f5e2251f39a78218943c2c9e54fff9c2c552a7ce2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:01:24.532415Z","signature_b64":"6PyT2QcaDJU/VFzdMeYHq92+/aBbDNGELTe7U7bmfOHVMpOFaN4mzYmMQXYo87evMt+lWkUffy0H5jq7voGdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4425e837bde1ff232a6d58b0b50520fa04cf69cb92ce1e762b9cfd37a0a489d","last_reissued_at":"2026-07-05T08:01:24.532006Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:01:24.532006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andras Molnar, Jose Garre Rubio, Yoshiko Ogata","submitted_at":"2024-03-27T13:54:45Z","abstract_excerpt":"We consider the classification problem of quantum spin chains invariant under local decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated to them. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological (SPT) phases. We prove that these invariants coincide with the ones of [J. Garre Rubio et al, Q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18573","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/2403.18573/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":"2403.18573","created_at":"2026-07-05T08:01:24.532056+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.18573v1","created_at":"2026-07-05T08:01:24.532056+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18573","created_at":"2026-07-05T08:01:24.532056+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRBF5A333YP7","created_at":"2026-07-05T08:01:24.532056+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRBF5A333YP7EMVG","created_at":"2026-07-05T08:01:24.532056+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRBF5A33","created_at":"2026-07-05T08:01:24.532056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.27193","citing_title":"Algebras of order parameters in one-dimensional spin systems","ref_index":118,"is_internal_anchor":false},{"citing_arxiv_id":"2605.28925","citing_title":"A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems","ref_index":80,"is_internal_anchor":false},{"citing_arxiv_id":"2405.15648","citing_title":"Self-$G$-ality in 1+1 dimensions","ref_index":65,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6","json":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6.json","graph_json":"https://pith.science/api/pith-number/WRBF5A333YP7EMVG2WFQWUCSB6/graph.json","events_json":"https://pith.science/api/pith-number/WRBF5A333YP7EMVG2WFQWUCSB6/events.json","paper":"https://pith.science/paper/WRBF5A33"},"agent_actions":{"view_html":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6","download_json":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6.json","view_paper":"https://pith.science/paper/WRBF5A33","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.18573&json=true","fetch_graph":"https://pith.science/api/pith-number/WRBF5A333YP7EMVG2WFQWUCSB6/graph.json","fetch_events":"https://pith.science/api/pith-number/WRBF5A333YP7EMVG2WFQWUCSB6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6/action/storage_attestation","attest_author":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6/action/author_attestation","sign_citation":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6/action/citation_signature","submit_replication":"https://pith.science/pith/WRBF5A333YP7EMVG2WFQWUCSB6/action/replication_record"}},"created_at":"2026-07-05T08:01:24.532056+00:00","updated_at":"2026-07-05T08:01:24.532056+00:00"}