{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HD3TTSB2RFEHNLLSHHDMESGR2S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"89587423a10176c1eac9b344b22b10ef159ff706950a46b4b142489c269642ae","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-09-02T09:41:13Z","title_canon_sha256":"3bf032ba0379c2c07be4a3c95f30c7ccbe6c0633d261c7387d446c266191eaad"},"schema_version":"1.0","source":{"id":"2409.01112","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01112","created_at":"2026-07-05T09:16:52Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01112v2","created_at":"2026-07-05T09:16:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01112","created_at":"2026-07-05T09:16:52Z"},{"alias_kind":"pith_short_12","alias_value":"HD3TTSB2RFEH","created_at":"2026-07-05T09:16:52Z"},{"alias_kind":"pith_short_16","alias_value":"HD3TTSB2RFEHNLLS","created_at":"2026-07-05T09:16:52Z"},{"alias_kind":"pith_short_8","alias_value":"HD3TTSB2","created_at":"2026-07-05T09:16:52Z"}],"graph_snapshots":[{"event_id":"sha256:b2d6b5f5999cbb87b5f69cc426aeca2cd5408fcb1df3bb6bdf3869782acb54c8","target":"graph","created_at":"2026-07-05T09:16:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.01112/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Symmetry protected states (SPT's) of quantum spin systems were studied by several authors. For one-dimensional systems (spin chains), there is an essentially complete and rigorous understanding: SPT's corresponding to finite on-site symmetry groups $G$ are classified by the second cohomology group $H^2(G,U(1))$, as established by Kapustin et al. [J. Math. Phys. (2021)]. We extend this result to the case of compact topological symmetry groups $G$. We also strengthen the existing results in the sense that our classification results holds within the class of spin chains with locally bounded on-si","authors_text":"Bruno de Oliveira Carvalho, Tijl Jappens, Wojciech De Roeck","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-09-02T09:41:13Z","title":"Classification of symmetry protected states of quantum spin chains for continuous symmetry groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01112","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8759e2624f34d28f65a032d317fdda69615280c4d1553cad827394d9701dbc90","target":"record","created_at":"2026-07-05T09:16:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"89587423a10176c1eac9b344b22b10ef159ff706950a46b4b142489c269642ae","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-09-02T09:41:13Z","title_canon_sha256":"3bf032ba0379c2c07be4a3c95f30c7ccbe6c0633d261c7387d446c266191eaad"},"schema_version":"1.0","source":{"id":"2409.01112","kind":"arxiv","version":2}},"canonical_sha256":"38f739c83a894876ad7239c6c248d1d494701fe70e71280b3e35bd1030112c7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38f739c83a894876ad7239c6c248d1d494701fe70e71280b3e35bd1030112c7c","first_computed_at":"2026-07-05T09:16:52.183642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:16:52.183642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PKtPvqslgU8Y8mYsSuYlOPJncBqFdae2HxXzalO9+QNFw4MIjwL4ubgaN2+JBAGw66Ofjm+0PAgAu+YHejnGAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:16:52.184158Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.01112","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8759e2624f34d28f65a032d317fdda69615280c4d1553cad827394d9701dbc90","sha256:b2d6b5f5999cbb87b5f69cc426aeca2cd5408fcb1df3bb6bdf3869782acb54c8"],"state_sha256":"81f66348d90b92f086ee6e045ce998ca85a0b2ea42eab7f1be06e31eed314303"}