{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6BI334E4R5MKGFBLPSHXVQU2B2","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":"1c93f676a6be699953850132bfc5e0e21385a972af7f62e2ff171d94a5e2b35e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-11T18:30:12Z","title_canon_sha256":"06b4b6ea152ed0348ba010319cbe1ce773cdc614e83378f67398e6c6663c31f3"},"schema_version":"1.0","source":{"id":"1206.2308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2308","created_at":"2026-05-18T03:53:52Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2308v1","created_at":"2026-05-18T03:53:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2308","created_at":"2026-05-18T03:53:52Z"},{"alias_kind":"pith_short_12","alias_value":"6BI334E4R5MK","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6BI334E4R5MKGFBL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6BI334E4","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:c6057e27cce6c930c018f0e580c32445afa177219ad2d8722b1a27103b799adb","target":"graph","created_at":"2026-05-18T03:53:52Z","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"},"paper":{"abstract_excerpt":"In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Turaev-Viro theory on a surface with boundary.","authors_text":"Alexander Kirillov Jr, Benjamin Balsam","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-11T18:30:12Z","title":"Kitaev's Lattice Model and Turaev-Viro TQFTs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2308","kind":"arxiv","version":1},"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:e6af57960fb6447abb181686b3d9ba52b586963acbc8a75c6a7283db61df6f9e","target":"record","created_at":"2026-05-18T03:53:52Z","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":"1c93f676a6be699953850132bfc5e0e21385a972af7f62e2ff171d94a5e2b35e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-11T18:30:12Z","title_canon_sha256":"06b4b6ea152ed0348ba010319cbe1ce773cdc614e83378f67398e6c6663c31f3"},"schema_version":"1.0","source":{"id":"1206.2308","kind":"arxiv","version":1}},"canonical_sha256":"f051bdf09c8f58a3142b7c8f7ac29a0e9123aee6f53ca827fc291917c890ea12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f051bdf09c8f58a3142b7c8f7ac29a0e9123aee6f53ca827fc291917c890ea12","first_computed_at":"2026-05-18T03:53:52.950342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:52.950342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f8UCatuFzwN/iyhq4blYeJg8YUJ3m9RdZQUPoylyPzvMXIn3KgNXTfCeMYNB6EcNx+8Ivb3dPxdMbIJnkeMDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:52.950826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6af57960fb6447abb181686b3d9ba52b586963acbc8a75c6a7283db61df6f9e","sha256:c6057e27cce6c930c018f0e580c32445afa177219ad2d8722b1a27103b799adb"],"state_sha256":"c98f4cb44ff011d1e28e08cb11be5a8c4e91d69a38d539a0a9516538b16eda87"}