{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:VNCZLQ6O37G4KQO2CWFTPEKJOE","short_pith_number":"pith:VNCZLQ6O","schema_version":"1.0","canonical_sha256":"ab4595c3cedfcdc541da158b37914971202926609ca9fa844467ed3ef3f013b7","source":{"kind":"arxiv","id":"math/0404135","version":2},"attestation_state":"computed","paper":{"title":"Ozsvath-Szabo invariants and tight contact three-manifolds, I","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Andras I Stipsicz, Paolo Lisca","submitted_at":"2004-04-06T15:35:01Z","abstract_excerpt":"Let S^3_r(K) be the oriented 3--manifold obtained by rational r-surgery on a knot K in S^3. Using the contact Ozsvath-Szabo invariants we prove, for a class of knots K containing all the algebraic knots, that S^3_r(K) carries positive, tight contact structures for every r not= 2g_s(K)-1, where g_s(K) is the slice genus of K. This implies, in particular, that the Brieskorn spheres -Sigma(2,3,4) and -Sigma(2,3,3) carry tight, positive contact structures. As an application of our main result we show that for each m in N there exists a Seifert fibered rational homology 3-sphere M_m carrying at lea"},"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/0404135","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2004-04-06T15:35:01Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"6a2435d2287aad80ca113c37070543c70e8476d037dff451dc313deaf3deeada","abstract_canon_sha256":"f4c45f9822951dff90a6650779c4708feaebcb06db8f5b142d2ef7d678fca059"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:00.132876Z","signature_b64":"Qa651Qg+5FBxPwECUoAmfLg242UmgVKzad3H3lOcsM/zXHiV74pAp3rkO6nUZjQNi2vBnLVbpDYr3Ye35OngAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab4595c3cedfcdc541da158b37914971202926609ca9fa844467ed3ef3f013b7","last_reissued_at":"2026-05-18T02:38:00.132486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:00.132486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ozsvath-Szabo invariants and tight contact three-manifolds, I","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Andras I Stipsicz, Paolo Lisca","submitted_at":"2004-04-06T15:35:01Z","abstract_excerpt":"Let S^3_r(K) be the oriented 3--manifold obtained by rational r-surgery on a knot K in S^3. Using the contact Ozsvath-Szabo invariants we prove, for a class of knots K containing all the algebraic knots, that S^3_r(K) carries positive, tight contact structures for every r not= 2g_s(K)-1, where g_s(K) is the slice genus of K. This implies, in particular, that the Brieskorn spheres -Sigma(2,3,4) and -Sigma(2,3,3) carry tight, positive contact structures. As an application of our main result we show that for each m in N there exists a Seifert fibered rational homology 3-sphere M_m carrying at lea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404135","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":"math/0404135","created_at":"2026-05-18T02:38:00.132545+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0404135v2","created_at":"2026-05-18T02:38:00.132545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404135","created_at":"2026-05-18T02:38:00.132545+00:00"},{"alias_kind":"pith_short_12","alias_value":"VNCZLQ6O37G4","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"VNCZLQ6O37G4KQO2","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"VNCZLQ6O","created_at":"2026-05-18T12:25:52.687210+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/VNCZLQ6O37G4KQO2CWFTPEKJOE","json":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE.json","graph_json":"https://pith.science/api/pith-number/VNCZLQ6O37G4KQO2CWFTPEKJOE/graph.json","events_json":"https://pith.science/api/pith-number/VNCZLQ6O37G4KQO2CWFTPEKJOE/events.json","paper":"https://pith.science/paper/VNCZLQ6O"},"agent_actions":{"view_html":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE","download_json":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE.json","view_paper":"https://pith.science/paper/VNCZLQ6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0404135&json=true","fetch_graph":"https://pith.science/api/pith-number/VNCZLQ6O37G4KQO2CWFTPEKJOE/graph.json","fetch_events":"https://pith.science/api/pith-number/VNCZLQ6O37G4KQO2CWFTPEKJOE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE/action/storage_attestation","attest_author":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE/action/author_attestation","sign_citation":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE/action/citation_signature","submit_replication":"https://pith.science/pith/VNCZLQ6O37G4KQO2CWFTPEKJOE/action/replication_record"}},"created_at":"2026-05-18T02:38:00.132545+00:00","updated_at":"2026-05-18T02:38:00.132545+00:00"}