{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XI54VUF5RTP6IICDF5IEP2E5BV","short_pith_number":"pith:XI54VUF5","schema_version":"1.0","canonical_sha256":"ba3bcad0bd8cdfe420432f5047e89d0d5e1b96a47a5222601932ec9b21246dff","source":{"kind":"arxiv","id":"1504.00922","version":2},"attestation_state":"computed","paper":{"title":"Lagrangian cobordism in Lefschetz fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Octav Cornea, Paul Biran","submitted_at":"2015-04-03T19:54:42Z","abstract_excerpt":"Given a symplectic manifold $(M^{2n},\\omega)$ we study Lagrangian cobordisms $V\\subset E$ where $E$ is the total space of a Lefschetz fibration having $M$ as generic fiber. We prove a generation result for these cobordisms in the appropriate derived Fukaya category. As a corollary, we analyze the relations among the Lagrangian submanifolds $L\\subset M$ that are induced by these cobordisms. This leads to a unified treatment - and a generalization - of the two types of relations among Lagrangian submanifolds of $M$ that were previously identified in the literature: those associated to Dehn twist"},"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":"1504.00922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-03T19:54:42Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6103cd8c518a990904acd9b3ae87b30fffc63686e1cdc0298e130bb6f2b01b61","abstract_canon_sha256":"3b07eefb20c0b3b5782552f0e41e6bae5c135ec9fe091cde4c3969c568aaa31e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:10.319843Z","signature_b64":"D8iv7VGbTO3HWkFuHbVUJ9MrA3zkjfSIws/eem0J+9IbC9s5iObnxJfct5Mj8xA2v1oXKZ2qKn+k6iUsP5+KCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba3bcad0bd8cdfe420432f5047e89d0d5e1b96a47a5222601932ec9b21246dff","last_reissued_at":"2026-05-18T01:14:10.318987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:10.318987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lagrangian cobordism in Lefschetz fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Octav Cornea, Paul Biran","submitted_at":"2015-04-03T19:54:42Z","abstract_excerpt":"Given a symplectic manifold $(M^{2n},\\omega)$ we study Lagrangian cobordisms $V\\subset E$ where $E$ is the total space of a Lefschetz fibration having $M$ as generic fiber. We prove a generation result for these cobordisms in the appropriate derived Fukaya category. As a corollary, we analyze the relations among the Lagrangian submanifolds $L\\subset M$ that are induced by these cobordisms. This leads to a unified treatment - and a generalization - of the two types of relations among Lagrangian submanifolds of $M$ that were previously identified in the literature: those associated to Dehn twist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00922","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":"1504.00922","created_at":"2026-05-18T01:14:10.319102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00922v2","created_at":"2026-05-18T01:14:10.319102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00922","created_at":"2026-05-18T01:14:10.319102+00:00"},{"alias_kind":"pith_short_12","alias_value":"XI54VUF5RTP6","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XI54VUF5RTP6IICD","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XI54VUF5","created_at":"2026-05-18T12:29:50.041715+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/XI54VUF5RTP6IICDF5IEP2E5BV","json":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV.json","graph_json":"https://pith.science/api/pith-number/XI54VUF5RTP6IICDF5IEP2E5BV/graph.json","events_json":"https://pith.science/api/pith-number/XI54VUF5RTP6IICDF5IEP2E5BV/events.json","paper":"https://pith.science/paper/XI54VUF5"},"agent_actions":{"view_html":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV","download_json":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV.json","view_paper":"https://pith.science/paper/XI54VUF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00922&json=true","fetch_graph":"https://pith.science/api/pith-number/XI54VUF5RTP6IICDF5IEP2E5BV/graph.json","fetch_events":"https://pith.science/api/pith-number/XI54VUF5RTP6IICDF5IEP2E5BV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV/action/storage_attestation","attest_author":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV/action/author_attestation","sign_citation":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV/action/citation_signature","submit_replication":"https://pith.science/pith/XI54VUF5RTP6IICDF5IEP2E5BV/action/replication_record"}},"created_at":"2026-05-18T01:14:10.319102+00:00","updated_at":"2026-05-18T01:14:10.319102+00:00"}