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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","authors_text":"Fan Ding, Qiang Zhang, Youlin Li","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-08T13:21:04Z","title":"Tight contact structures on some bounded Seifert manifolds with minimal convex boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1900","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8be29235c9dcc2f38bae05a90678e5e19ce06a445d9bbbde148866adeb3d3d2d","target":"record","created_at":"2026-05-18T04:08:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6868bc3dbdd0e933cd04c314f402924516b5fe4d14c6cbc6aaed1b8e17871b9c","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-11-08T13:21:04Z","title_canon_sha256":"6e2c7995ac26b31d9c5df27b4e3fc1238bc3d92c8ef8a5f35aef8cb75141b61e"},"schema_version":"1.0","source":{"id":"1111.1900","kind":"arxiv","version":2}},"canonical_sha256":"854856bbedab98040d8d3966c400398cbe6dbf7104b3b257c02be870cd820fd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"854856bbedab98040d8d3966c400398cbe6dbf7104b3b257c02be870cd820fd1","first_computed_at":"2026-05-18T04:08:03.276603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:03.276603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jUrEZu3m0s/ra32hFQUQlArbnVzvdHYAIWNKeXqf8PiBx7TnPypGIbAtglFbfc6dw8BQM7b+lm6FXL5dd5CFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:03.277090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8be29235c9dcc2f38bae05a90678e5e19ce06a445d9bbbde148866adeb3d3d2d","sha256:d1f47b349e498d61c7ebb839ac3f12532f2dcf2f10efc5d4390ece577a975e33"],"state_sha256":"99ef426111478b2199c92ee03226ef4f4dcc87aca7a902e9b2b6ddb3745ab734"}