{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:WBEVPBZCOFTNCFLXZZ5GW6IW3N","short_pith_number":"pith:WBEVPBZC","schema_version":"1.0","canonical_sha256":"b0495787227166d11577ce7a6b7916db5502395386bd4d6a42c99281f0e3f923","source":{"kind":"arxiv","id":"0906.3487","version":3},"attestation_state":"computed","paper":{"title":"Tightness in contact metric 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.SG","authors_text":"John B. Etnyre, Patrick Massot, Rafal Komendarczyk","submitted_at":"2009-06-18T17:48:37Z","abstract_excerpt":"This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact geometry. Specifically, if a given three dimensional contact manifold (M,\\xi) admits a complete compatible Riemannian metric of positive 4/9-pinched curvature then the underlying contact structure \\xi is tight; in particular, the contact structure pulled back to the universal cover is the standard contact structure on S^3. We also describe geometric conditions in"},"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":"0906.3487","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-06-18T17:48:37Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"4b6d9581ebc91edd30ed7fe3748f656147aa23e9bcace1467d8ddc2d5881dd02","abstract_canon_sha256":"2f63b40e62a4e35e0ae9566a7914312dabedd966c3e5c966b21ef68f3c1b5523"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:24.769494Z","signature_b64":"uO2zaXq4OzuL0GJiNrV91084hDN/vDEcrBdY0qcIJGygWK9ICWUjtT2PbM12jmIW7oW6spv1SPuWWfHC+o3vBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0495787227166d11577ce7a6b7916db5502395386bd4d6a42c99281f0e3f923","last_reissued_at":"2026-05-18T01:33:24.768872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:24.768872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tightness in contact metric 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.SG","authors_text":"John B. Etnyre, Patrick Massot, Rafal Komendarczyk","submitted_at":"2009-06-18T17:48:37Z","abstract_excerpt":"This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact geometry. Specifically, if a given three dimensional contact manifold (M,\\xi) admits a complete compatible Riemannian metric of positive 4/9-pinched curvature then the underlying contact structure \\xi is tight; in particular, the contact structure pulled back to the universal cover is the standard contact structure on S^3. We also describe geometric conditions in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3487","kind":"arxiv","version":3},"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":"0906.3487","created_at":"2026-05-18T01:33:24.768971+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.3487v3","created_at":"2026-05-18T01:33:24.768971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3487","created_at":"2026-05-18T01:33:24.768971+00:00"},{"alias_kind":"pith_short_12","alias_value":"WBEVPBZCOFTN","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"WBEVPBZCOFTNCFLX","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"WBEVPBZC","created_at":"2026-05-18T12:26:02.257875+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/WBEVPBZCOFTNCFLXZZ5GW6IW3N","json":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N.json","graph_json":"https://pith.science/api/pith-number/WBEVPBZCOFTNCFLXZZ5GW6IW3N/graph.json","events_json":"https://pith.science/api/pith-number/WBEVPBZCOFTNCFLXZZ5GW6IW3N/events.json","paper":"https://pith.science/paper/WBEVPBZC"},"agent_actions":{"view_html":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N","download_json":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N.json","view_paper":"https://pith.science/paper/WBEVPBZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.3487&json=true","fetch_graph":"https://pith.science/api/pith-number/WBEVPBZCOFTNCFLXZZ5GW6IW3N/graph.json","fetch_events":"https://pith.science/api/pith-number/WBEVPBZCOFTNCFLXZZ5GW6IW3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N/action/storage_attestation","attest_author":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N/action/author_attestation","sign_citation":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N/action/citation_signature","submit_replication":"https://pith.science/pith/WBEVPBZCOFTNCFLXZZ5GW6IW3N/action/replication_record"}},"created_at":"2026-05-18T01:33:24.768971+00:00","updated_at":"2026-05-18T01:33:24.768971+00:00"}