{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:C2H3QEAG3UGIHSU3OJWAWH6R7J","short_pith_number":"pith:C2H3QEAG","schema_version":"1.0","canonical_sha256":"168fb81006dd0c83ca9b726c0b1fd1fa547fea92d29fcf885534daf3ce5015a5","source":{"kind":"arxiv","id":"math/0412511","version":4},"attestation_state":"computed","paper":{"title":"Links, two-handles, and four-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bruno Martelli","submitted_at":"2004-12-28T12:35:32Z","abstract_excerpt":"We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth cobordisms between two given closed 3-manifolds.\n  As a consequence, there are finitely many smooth closed 4-manifolds constructed from some Kirby diagram with bounded number of crossings, discs, and strands, or from some Turaev special shadow with bounded number of vertices. (These are the 4-dimensional analogues of Heegaard diagrams and special spines for 3-ma"},"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":"math/0412511","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2004-12-28T12:35:32Z","cross_cats_sorted":[],"title_canon_sha256":"ff62f5c7d068aeb428b3dbba98ef6b708c0ffcaad0ef51abdc549a6762dfd193","abstract_canon_sha256":"87bd98583c8fc4594134887b89a173dcaa9eba2b9139e22fceaa6c34e879dc9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:06.184538Z","signature_b64":"kLy82k/rsqdyiG7wsbXkXBvOzafqB7qupLSG+4kuDUb+Emg/0iBDoVLm+CsR5jBrfcD58rhD62zT39+lq7HNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"168fb81006dd0c83ca9b726c0b1fd1fa547fea92d29fcf885534daf3ce5015a5","last_reissued_at":"2026-05-18T04:14:06.184025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:06.184025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Links, two-handles, and four-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bruno Martelli","submitted_at":"2004-12-28T12:35:32Z","abstract_excerpt":"We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth cobordisms between two given closed 3-manifolds.\n  As a consequence, there are finitely many smooth closed 4-manifolds constructed from some Kirby diagram with bounded number of crossings, discs, and strands, or from some Turaev special shadow with bounded number of vertices. (These are the 4-dimensional analogues of Heegaard diagrams and special spines for 3-ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412511","kind":"arxiv","version":4},"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":"math/0412511","created_at":"2026-05-18T04:14:06.184100+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0412511v4","created_at":"2026-05-18T04:14:06.184100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412511","created_at":"2026-05-18T04:14:06.184100+00:00"},{"alias_kind":"pith_short_12","alias_value":"C2H3QEAG3UGI","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"C2H3QEAG3UGIHSU3","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"C2H3QEAG","created_at":"2026-05-18T12:25:52.051335+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/C2H3QEAG3UGIHSU3OJWAWH6R7J","json":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J.json","graph_json":"https://pith.science/api/pith-number/C2H3QEAG3UGIHSU3OJWAWH6R7J/graph.json","events_json":"https://pith.science/api/pith-number/C2H3QEAG3UGIHSU3OJWAWH6R7J/events.json","paper":"https://pith.science/paper/C2H3QEAG"},"agent_actions":{"view_html":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J","download_json":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J.json","view_paper":"https://pith.science/paper/C2H3QEAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0412511&json=true","fetch_graph":"https://pith.science/api/pith-number/C2H3QEAG3UGIHSU3OJWAWH6R7J/graph.json","fetch_events":"https://pith.science/api/pith-number/C2H3QEAG3UGIHSU3OJWAWH6R7J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J/action/storage_attestation","attest_author":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J/action/author_attestation","sign_citation":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J/action/citation_signature","submit_replication":"https://pith.science/pith/C2H3QEAG3UGIHSU3OJWAWH6R7J/action/replication_record"}},"created_at":"2026-05-18T04:14:06.184100+00:00","updated_at":"2026-05-18T04:14:06.184100+00:00"}