{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1996:BAN6XCTQSNVDODQRE7GKW65MUM","short_pith_number":"pith:BAN6XCTQ","schema_version":"1.0","canonical_sha256":"081beb8a70936a370e1127ccab7baca30d4891f4a4ed6d739eb39bc044c61051","source":{"kind":"arxiv","id":"q-alg/9601021","version":2},"attestation_state":"computed","paper":{"title":"Genealogy of Nonperturbative Quantum-Invariants of 3-Manifolds: The Surgical Family","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"Thomas Kerler","submitted_at":"1996-01-21T02:36:20Z","abstract_excerpt":"We study the relations between the invariants $\\tau_{RT}$, $\\tau_{HKR}$, and\n $\\tau_L$ of Reshetikhin-Turaev, Hennings-Kauffman-Radford, and Lyubashenko,\n respectively. In particular, we discuss explicitly how $\\tau_L$ specializes to $\\tau_{RT}$ for semisimple categories and to $\\tau_{HKR}$ for Tannakian categories. We give arguments for that $\\tau_L$ is the most general invariant that stems from an extended TQFT. We introduce a canonical, central element, {\\sf Q}, for a quasi-triangular Hopf algebra, $\\A$, that allows us to apply the Hennings algorithm directly, in order to compute $\\tau_{RT}"},"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":"q-alg/9601021","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1996-01-21T02:36:20Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"f6eeb76e5579103885ff23fdadb622ba619b7132efededc568927420e90a1ef1","abstract_canon_sha256":"1f5514239e1cebf54e397625be2117bc3c01889cfcef613a2eb4989fa2c68a17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:07.561987Z","signature_b64":"uw+YGRPyY+Ppkv8wgUFTCVyfYutnhlQwwN1OuUNMtCyqo7h2wNPYHKy4zqkRcccXQ2y+KsjxOrOuFI2TE5ClAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"081beb8a70936a370e1127ccab7baca30d4891f4a4ed6d739eb39bc044c61051","last_reissued_at":"2026-05-18T01:05:07.561224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:07.561224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Genealogy of Nonperturbative Quantum-Invariants of 3-Manifolds: The Surgical Family","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"Thomas Kerler","submitted_at":"1996-01-21T02:36:20Z","abstract_excerpt":"We study the relations between the invariants $\\tau_{RT}$, $\\tau_{HKR}$, and\n $\\tau_L$ of Reshetikhin-Turaev, Hennings-Kauffman-Radford, and Lyubashenko,\n respectively. In particular, we discuss explicitly how $\\tau_L$ specializes to $\\tau_{RT}$ for semisimple categories and to $\\tau_{HKR}$ for Tannakian categories. We give arguments for that $\\tau_L$ is the most general invariant that stems from an extended TQFT. We introduce a canonical, central element, {\\sf Q}, for a quasi-triangular Hopf algebra, $\\A$, that allows us to apply the Hennings algorithm directly, in order to compute $\\tau_{RT}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9601021","kind":"arxiv","version":2},"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":"q-alg/9601021","created_at":"2026-05-18T01:05:07.561372+00:00"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9601021v2","created_at":"2026-05-18T01:05:07.561372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9601021","created_at":"2026-05-18T01:05:07.561372+00:00"},{"alias_kind":"pith_short_12","alias_value":"BAN6XCTQSNVD","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_16","alias_value":"BAN6XCTQSNVDODQR","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_8","alias_value":"BAN6XCTQ","created_at":"2026-05-18T12:25:47.700082+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/BAN6XCTQSNVDODQRE7GKW65MUM","json":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM.json","graph_json":"https://pith.science/api/pith-number/BAN6XCTQSNVDODQRE7GKW65MUM/graph.json","events_json":"https://pith.science/api/pith-number/BAN6XCTQSNVDODQRE7GKW65MUM/events.json","paper":"https://pith.science/paper/BAN6XCTQ"},"agent_actions":{"view_html":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM","download_json":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM.json","view_paper":"https://pith.science/paper/BAN6XCTQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=q-alg/9601021&json=true","fetch_graph":"https://pith.science/api/pith-number/BAN6XCTQSNVDODQRE7GKW65MUM/graph.json","fetch_events":"https://pith.science/api/pith-number/BAN6XCTQSNVDODQRE7GKW65MUM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM/action/storage_attestation","attest_author":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM/action/author_attestation","sign_citation":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM/action/citation_signature","submit_replication":"https://pith.science/pith/BAN6XCTQSNVDODQRE7GKW65MUM/action/replication_record"}},"created_at":"2026-05-18T01:05:07.561372+00:00","updated_at":"2026-05-18T01:05:07.561372+00:00"}