{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TBSIPRWU4URQ6ENMWSZBUOZ3X2","short_pith_number":"pith:TBSIPRWU","schema_version":"1.0","canonical_sha256":"986487c6d4e5230f11acb4b21a3b3bbe8a74d12fece52fec4cc827fce7f436da","source":{"kind":"arxiv","id":"1509.05945","version":1},"attestation_state":"computed","paper":{"title":"On the classification of Heegaard splittings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Daniel Ketover, David Gabai, Tobias Holck Colding","submitted_at":"2015-09-19T22:41:03Z","abstract_excerpt":"The long standing classification problem in the theory of Heegaard splittings of 3-manifolds is to exhibit for each closed 3-manifold a complete list, without duplication, of all its irreducible Heegaard surfaces, up to isotopy. We solve this problem for non Haken hyperbolic 3-manifolds."},"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":"1509.05945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-19T22:41:03Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"43d68d3d565d781c8299741652b3c28ea23663a627a40da9c371de1ad56a8356","abstract_canon_sha256":"d605a0316e53fdaf5f20c71cafa41fcc8c0fcd97299bc723b58d1b3c9af40fa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:46.065989Z","signature_b64":"Lw6qgaVITX/pRVrP2Omxw4In/9kYYGAxxgjCdaY2npPDK+YD2NL51B3ZtYL5TVPlBORoB1BZ+RPhxhfLpX/zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"986487c6d4e5230f11acb4b21a3b3bbe8a74d12fece52fec4cc827fce7f436da","last_reissued_at":"2026-05-18T00:00:46.065611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:46.065611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the classification of Heegaard splittings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Daniel Ketover, David Gabai, Tobias Holck Colding","submitted_at":"2015-09-19T22:41:03Z","abstract_excerpt":"The long standing classification problem in the theory of Heegaard splittings of 3-manifolds is to exhibit for each closed 3-manifold a complete list, without duplication, of all its irreducible Heegaard surfaces, up to isotopy. We solve this problem for non Haken hyperbolic 3-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05945","kind":"arxiv","version":1},"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":"1509.05945","created_at":"2026-05-18T00:00:46.065669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.05945v1","created_at":"2026-05-18T00:00:46.065669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05945","created_at":"2026-05-18T00:00:46.065669+00:00"},{"alias_kind":"pith_short_12","alias_value":"TBSIPRWU4URQ","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TBSIPRWU4URQ6ENM","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TBSIPRWU","created_at":"2026-05-18T12:29:42.218222+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/TBSIPRWU4URQ6ENMWSZBUOZ3X2","json":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2.json","graph_json":"https://pith.science/api/pith-number/TBSIPRWU4URQ6ENMWSZBUOZ3X2/graph.json","events_json":"https://pith.science/api/pith-number/TBSIPRWU4URQ6ENMWSZBUOZ3X2/events.json","paper":"https://pith.science/paper/TBSIPRWU"},"agent_actions":{"view_html":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2","download_json":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2.json","view_paper":"https://pith.science/paper/TBSIPRWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.05945&json=true","fetch_graph":"https://pith.science/api/pith-number/TBSIPRWU4URQ6ENMWSZBUOZ3X2/graph.json","fetch_events":"https://pith.science/api/pith-number/TBSIPRWU4URQ6ENMWSZBUOZ3X2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2/action/storage_attestation","attest_author":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2/action/author_attestation","sign_citation":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2/action/citation_signature","submit_replication":"https://pith.science/pith/TBSIPRWU4URQ6ENMWSZBUOZ3X2/action/replication_record"}},"created_at":"2026-05-18T00:00:46.065669+00:00","updated_at":"2026-05-18T00:00:46.065669+00:00"}