{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:YXLMGATNYNFMLS4WAE2NEZQDMT","short_pith_number":"pith:YXLMGATN","schema_version":"1.0","canonical_sha256":"c5d6c3026dc34ac5cb960134d2660364c1e2f2f92f283724288d75e2a38dc014","source":{"kind":"arxiv","id":"2202.06243","version":3},"attestation_state":"computed","paper":{"title":"The Lieb-Schultz-Mattis Theorem: A Topological Point of View","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hal Tasaki","submitted_at":"2022-02-13T07:49:31Z","abstract_excerpt":"We review the Lieb-Schultz-Mattis theorem and its variants, which are no-go theorems that state that a quantum many-body system with certain conditions cannot have a locally-unique gapped ground state. We restrict ourselves to one-dimensional quantum spin systems and discuss both the generalized Lieb-Schultz-Mattis theorem for models with U(1) symmetry and the extended Lieb-Schultz-Mattis theorem for models with discrete symmetry. We also discuss the implication of the same arguments to systems on the infinite cylinder, both with the periodic boundary conditions and with the spiral boundary co"},"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":"2202.06243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2022-02-13T07:49:31Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"2924e2480835f3d81660912bc7c2322872db23056b724e51c3f38c6def33df50","abstract_canon_sha256":"683a1c3485904091396cd41d8864fb53f9977778adbd62f6dc5db5014c8998a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:49:11.273579Z","signature_b64":"C7HaEPPz/o7h1rf+10XiHS591YHgbT7AWIvloI29xjZpaRCwFTBRGQdbAYUf3duI+5ZNgDeiEPw/RC5Qr13oCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5d6c3026dc34ac5cb960134d2660364c1e2f2f92f283724288d75e2a38dc014","last_reissued_at":"2026-07-05T04:49:11.273149Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:49:11.273149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Lieb-Schultz-Mattis Theorem: A Topological Point of View","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hal Tasaki","submitted_at":"2022-02-13T07:49:31Z","abstract_excerpt":"We review the Lieb-Schultz-Mattis theorem and its variants, which are no-go theorems that state that a quantum many-body system with certain conditions cannot have a locally-unique gapped ground state. We restrict ourselves to one-dimensional quantum spin systems and discuss both the generalized Lieb-Schultz-Mattis theorem for models with U(1) symmetry and the extended Lieb-Schultz-Mattis theorem for models with discrete symmetry. We also discuss the implication of the same arguments to systems on the infinite cylinder, both with the periodic boundary conditions and with the spiral boundary co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06243","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/2202.06243/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":"2202.06243","created_at":"2026-07-05T04:49:11.273206+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.06243v3","created_at":"2026-07-05T04:49:11.273206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06243","created_at":"2026-07-05T04:49:11.273206+00:00"},{"alias_kind":"pith_short_12","alias_value":"YXLMGATNYNFM","created_at":"2026-07-05T04:49:11.273206+00:00"},{"alias_kind":"pith_short_16","alias_value":"YXLMGATNYNFMLS4W","created_at":"2026-07-05T04:49:11.273206+00:00"},{"alias_kind":"pith_short_8","alias_value":"YXLMGATN","created_at":"2026-07-05T04:49:11.273206+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"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":69,"is_internal_anchor":false},{"citing_arxiv_id":"2407.17041","citing_title":"The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped","ref_index":33,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT","json":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT.json","graph_json":"https://pith.science/api/pith-number/YXLMGATNYNFMLS4WAE2NEZQDMT/graph.json","events_json":"https://pith.science/api/pith-number/YXLMGATNYNFMLS4WAE2NEZQDMT/events.json","paper":"https://pith.science/paper/YXLMGATN"},"agent_actions":{"view_html":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT","download_json":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT.json","view_paper":"https://pith.science/paper/YXLMGATN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.06243&json=true","fetch_graph":"https://pith.science/api/pith-number/YXLMGATNYNFMLS4WAE2NEZQDMT/graph.json","fetch_events":"https://pith.science/api/pith-number/YXLMGATNYNFMLS4WAE2NEZQDMT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT/action/storage_attestation","attest_author":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT/action/author_attestation","sign_citation":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT/action/citation_signature","submit_replication":"https://pith.science/pith/YXLMGATNYNFMLS4WAE2NEZQDMT/action/replication_record"}},"created_at":"2026-07-05T04:49:11.273206+00:00","updated_at":"2026-07-05T04:49:11.273206+00:00"}