{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QVEFNO7NVOMAIDMNHFTMIABZRS","short_pith_number":"pith:QVEFNO7N","schema_version":"1.0","canonical_sha256":"854856bbedab98040d8d3966c400398cbe6dbf7104b3b257c02be870cd820fd1","source":{"kind":"arxiv","id":"1111.1900","version":2},"attestation_state":"computed","paper":{"title":"Tight contact structures on some bounded Seifert manifolds with minimal convex boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Fan Ding, Qiang Zhang, Youlin Li","submitted_at":"2011-11-08T13:21:04Z","abstract_excerpt":"We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds $N=M(D^{2}; r_1, r_2)$ with minimal convex boundary of slope $s$ and Giroux torsion 0 along $\\partial N$, where $r_1,r_2\\in (0,1)\\cap\\mathbb{Q}$, in the following cases:\n  (1) $s\\in(-\\infty, 0)\\cup[2, +\\infty)$;\n  (2) $s\\in[0, 1)$ and $r_1,r_2\\in [1/2,1)$;\n  (3) $s\\in[1, 2)$ and $r_1,r_2\\in(0,1/2)$;\n  (4) $s=\\infty$ and $r_1=r_2=1/2$.\n  We also classify positive tight contact structures, up to isotopy fixing the boundary, on $M(D^2;1/2,1/2)$ with minimal convex boundary of arbitrary slope and Gir"},"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":"1111.1900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-08T13:21:04Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"6e2c7995ac26b31d9c5df27b4e3fc1238bc3d92c8ef8a5f35aef8cb75141b61e","abstract_canon_sha256":"6868bc3dbdd0e933cd04c314f402924516b5fe4d14c6cbc6aaed1b8e17871b9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:03.277090Z","signature_b64":"jUrEZu3m0s/ra32hFQUQlArbnVzvdHYAIWNKeXqf8PiBx7TnPypGIbAtglFbfc6dw8BQM7b+lm6FXL5dd5CFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"854856bbedab98040d8d3966c400398cbe6dbf7104b3b257c02be870cd820fd1","last_reissued_at":"2026-05-18T04:08:03.276603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:03.276603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight contact structures on some bounded Seifert manifolds with minimal convex boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Fan Ding, Qiang Zhang, Youlin Li","submitted_at":"2011-11-08T13:21:04Z","abstract_excerpt":"We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds $N=M(D^{2}; r_1, r_2)$ with minimal convex boundary of slope $s$ and Giroux torsion 0 along $\\partial N$, where $r_1,r_2\\in (0,1)\\cap\\mathbb{Q}$, in the following cases:\n  (1) $s\\in(-\\infty, 0)\\cup[2, +\\infty)$;\n  (2) $s\\in[0, 1)$ and $r_1,r_2\\in [1/2,1)$;\n  (3) $s\\in[1, 2)$ and $r_1,r_2\\in(0,1/2)$;\n  (4) $s=\\infty$ and $r_1=r_2=1/2$.\n  We also classify positive tight contact structures, up to isotopy fixing the boundary, on $M(D^2;1/2,1/2)$ with minimal convex boundary of arbitrary slope and Gir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1900","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":"1111.1900","created_at":"2026-05-18T04:08:03.276670+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1900v2","created_at":"2026-05-18T04:08:03.276670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1900","created_at":"2026-05-18T04:08:03.276670+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVEFNO7NVOMA","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVEFNO7NVOMAIDMN","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVEFNO7N","created_at":"2026-05-18T12:26:39.201973+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/QVEFNO7NVOMAIDMNHFTMIABZRS","json":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS.json","graph_json":"https://pith.science/api/pith-number/QVEFNO7NVOMAIDMNHFTMIABZRS/graph.json","events_json":"https://pith.science/api/pith-number/QVEFNO7NVOMAIDMNHFTMIABZRS/events.json","paper":"https://pith.science/paper/QVEFNO7N"},"agent_actions":{"view_html":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS","download_json":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS.json","view_paper":"https://pith.science/paper/QVEFNO7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1900&json=true","fetch_graph":"https://pith.science/api/pith-number/QVEFNO7NVOMAIDMNHFTMIABZRS/graph.json","fetch_events":"https://pith.science/api/pith-number/QVEFNO7NVOMAIDMNHFTMIABZRS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS/action/storage_attestation","attest_author":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS/action/author_attestation","sign_citation":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS/action/citation_signature","submit_replication":"https://pith.science/pith/QVEFNO7NVOMAIDMNHFTMIABZRS/action/replication_record"}},"created_at":"2026-05-18T04:08:03.276670+00:00","updated_at":"2026-05-18T04:08:03.276670+00:00"}