{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:E4YI2D5L43KSWZODP5ZWLQQW5L","short_pith_number":"pith:E4YI2D5L","schema_version":"1.0","canonical_sha256":"27308d0fabe6d52b65c37f7365c216eadfae2bbb569de61352ec8806a6e90da1","source":{"kind":"arxiv","id":"math/0305186","version":1},"attestation_state":"computed","paper":{"title":"On the coarse classification of tight contact structures","license":"","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.GT","authors_text":"Emmanuel Giroux, Ko Honda, Vincent Colin","submitted_at":"2003-05-13T17:15:33Z","abstract_excerpt":"We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures."},"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/0305186","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2003-05-13T17:15:33Z","cross_cats_sorted":["math.DG","math.SG"],"title_canon_sha256":"6854d5471e4013f9d75470c69330f198d7ccaa48c7a842f72304ecd2e6c2f5b1","abstract_canon_sha256":"97fbaa2497b6e7cdf0dd12a611225d7348e49f822f32fdd974f627beeeb987bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:18.552516Z","signature_b64":"TYs9+wmbQ8TvrZDxqW567Afku/NM7evA+k9csn/DNMobqYkYV81yTawNk+a77r8NKkoTNtgMHW2ipceujocNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27308d0fabe6d52b65c37f7365c216eadfae2bbb569de61352ec8806a6e90da1","last_reissued_at":"2026-07-04T14:37:18.552138Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:18.552138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the coarse classification of tight contact structures","license":"","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.GT","authors_text":"Emmanuel Giroux, Ko Honda, Vincent Colin","submitted_at":"2003-05-13T17:15:33Z","abstract_excerpt":"We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305186","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0305186/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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/0305186","created_at":"2026-07-04T14:37:18.552193+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0305186v1","created_at":"2026-07-04T14:37:18.552193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305186","created_at":"2026-07-04T14:37:18.552193+00:00"},{"alias_kind":"pith_short_12","alias_value":"E4YI2D5L43KS","created_at":"2026-07-04T14:37:18.552193+00:00"},{"alias_kind":"pith_short_16","alias_value":"E4YI2D5L43KSWZOD","created_at":"2026-07-04T14:37:18.552193+00:00"},{"alias_kind":"pith_short_8","alias_value":"E4YI2D5L","created_at":"2026-07-04T14:37:18.552193+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/E4YI2D5L43KSWZODP5ZWLQQW5L","json":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L.json","graph_json":"https://pith.science/api/pith-number/E4YI2D5L43KSWZODP5ZWLQQW5L/graph.json","events_json":"https://pith.science/api/pith-number/E4YI2D5L43KSWZODP5ZWLQQW5L/events.json","paper":"https://pith.science/paper/E4YI2D5L"},"agent_actions":{"view_html":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L","download_json":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L.json","view_paper":"https://pith.science/paper/E4YI2D5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0305186&json=true","fetch_graph":"https://pith.science/api/pith-number/E4YI2D5L43KSWZODP5ZWLQQW5L/graph.json","fetch_events":"https://pith.science/api/pith-number/E4YI2D5L43KSWZODP5ZWLQQW5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L/action/storage_attestation","attest_author":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L/action/author_attestation","sign_citation":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L/action/citation_signature","submit_replication":"https://pith.science/pith/E4YI2D5L43KSWZODP5ZWLQQW5L/action/replication_record"}},"created_at":"2026-07-04T14:37:18.552193+00:00","updated_at":"2026-07-04T14:37:18.552193+00:00"}