{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TNUZ4EAFMTBXA6TKJORFTRCJEE","short_pith_number":"pith:TNUZ4EAF","schema_version":"1.0","canonical_sha256":"9b699e100564c3707a6a4ba259c44921155ee76c4d9770190d947abd9582f37c","source":{"kind":"arxiv","id":"1611.01140","version":3},"attestation_state":"computed","paper":{"title":"The structure of fixed-point tensor network states characterizes patterns of long-range entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Ethan Lake, Yong-Shi Wu, Zhu-Xi Luo","submitted_at":"2016-11-03T19:41:44Z","abstract_excerpt":"The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological quantum field theory (TQFT). We show that a 2D fixed-point tensor network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the tensor network or the TQFT is made explicit in a form of holograp"},"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":"1611.01140","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-11-03T19:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"64c1e513e280f57fc05ce6f4623b23b35e0a03f59124589542d645a75564d921","abstract_canon_sha256":"81de923d4ed259d4719973964534680d0dd37cff58680ad8145b0237db9bfa8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:33.084327Z","signature_b64":"z6o3iaWjN8NVPYPkVDelO9Fk+dmN5NKV4ynYh8iUDenNB6zUG9yUhk1YhVVzW0/jvYBCN456e9KYpY+TTbf/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b699e100564c3707a6a4ba259c44921155ee76c4d9770190d947abd9582f37c","last_reissued_at":"2026-05-18T00:40:33.083523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:33.083523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The structure of fixed-point tensor network states characterizes patterns of long-range entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Ethan Lake, Yong-Shi Wu, Zhu-Xi Luo","submitted_at":"2016-11-03T19:41:44Z","abstract_excerpt":"The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological quantum field theory (TQFT). We show that a 2D fixed-point tensor network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the tensor network or the TQFT is made explicit in a form of holograp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01140","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":""},"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":"1611.01140","created_at":"2026-05-18T00:40:33.083641+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.01140v3","created_at":"2026-05-18T00:40:33.083641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01140","created_at":"2026-05-18T00:40:33.083641+00:00"},{"alias_kind":"pith_short_12","alias_value":"TNUZ4EAFMTBX","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"TNUZ4EAFMTBXA6TK","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"TNUZ4EAF","created_at":"2026-05-18T12:30:46.583412+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/TNUZ4EAFMTBXA6TKJORFTRCJEE","json":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE.json","graph_json":"https://pith.science/api/pith-number/TNUZ4EAFMTBXA6TKJORFTRCJEE/graph.json","events_json":"https://pith.science/api/pith-number/TNUZ4EAFMTBXA6TKJORFTRCJEE/events.json","paper":"https://pith.science/paper/TNUZ4EAF"},"agent_actions":{"view_html":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE","download_json":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE.json","view_paper":"https://pith.science/paper/TNUZ4EAF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.01140&json=true","fetch_graph":"https://pith.science/api/pith-number/TNUZ4EAFMTBXA6TKJORFTRCJEE/graph.json","fetch_events":"https://pith.science/api/pith-number/TNUZ4EAFMTBXA6TKJORFTRCJEE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE/action/storage_attestation","attest_author":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE/action/author_attestation","sign_citation":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE/action/citation_signature","submit_replication":"https://pith.science/pith/TNUZ4EAFMTBXA6TKJORFTRCJEE/action/replication_record"}},"created_at":"2026-05-18T00:40:33.083641+00:00","updated_at":"2026-05-18T00:40:33.083641+00:00"}