{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:QFPGSOTZNXVAU3ID7OBTIGEHXB","short_pith_number":"pith:QFPGSOTZ","schema_version":"1.0","canonical_sha256":"815e693a796dea0a6d03fb83341887b85497f52d694cdfefd90be7c8e26679f9","source":{"kind":"arxiv","id":"2110.12950","version":1},"attestation_state":"computed","paper":{"title":"Symplectic embeddings of 4-manifolds via Lefschetz fibrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Dishant M. Pancholi, Francisco Presas","submitted_at":"2021-10-25T13:39:16Z","abstract_excerpt":"In this article we study proper symplectic and iso-symplectic embeddings of $4$--manifolds in $6$--manifolds. We show that a closed orientable smooth $4$--manifold admitting a Lefschetz fibration over $\\C P^1$ admits a symplectic embedding in the symplectic manifold $(\\C P^1 \\times \\C P^1 \\times \\C P^1, \\omega_{pr}),$ where $\\omega_{pr}$ is the product symplectic form on $\\C P^1 \\times \\C P^1 \\times \\C P^1.$ We also show that there exists a sub-critical Weinstein $6$--manifold in which all finite type Weinstein $4$--manifolds admit iso-symplectic embeddings."},"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":"2110.12950","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2021-10-25T13:39:16Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"85bf6e16f5ce5222fc9f0e800347bd5c72939d2ca41996b4bc60ec038a1adf69","abstract_canon_sha256":"90699633b556b57287eb47ea5bf26e7b697c75c915c703dc010f1aba2bac1fe4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:25:25.682696Z","signature_b64":"3H++X4Z/GaLH/GJwpcwemad+JMfm0flUMhZVGv3TS+7I1AcYm+d3x5XbP9bHKrG//7l3/3i787aZvZzlpLn7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"815e693a796dea0a6d03fb83341887b85497f52d694cdfefd90be7c8e26679f9","last_reissued_at":"2026-07-05T03:25:25.682311Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:25:25.682311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic embeddings of 4-manifolds via Lefschetz fibrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Dishant M. Pancholi, Francisco Presas","submitted_at":"2021-10-25T13:39:16Z","abstract_excerpt":"In this article we study proper symplectic and iso-symplectic embeddings of $4$--manifolds in $6$--manifolds. We show that a closed orientable smooth $4$--manifold admitting a Lefschetz fibration over $\\C P^1$ admits a symplectic embedding in the symplectic manifold $(\\C P^1 \\times \\C P^1 \\times \\C P^1, \\omega_{pr}),$ where $\\omega_{pr}$ is the product symplectic form on $\\C P^1 \\times \\C P^1 \\times \\C P^1.$ We also show that there exists a sub-critical Weinstein $6$--manifold in which all finite type Weinstein $4$--manifolds admit iso-symplectic embeddings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12950","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/2110.12950/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":"2110.12950","created_at":"2026-07-05T03:25:25.682383+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.12950v1","created_at":"2026-07-05T03:25:25.682383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.12950","created_at":"2026-07-05T03:25:25.682383+00:00"},{"alias_kind":"pith_short_12","alias_value":"QFPGSOTZNXVA","created_at":"2026-07-05T03:25:25.682383+00:00"},{"alias_kind":"pith_short_16","alias_value":"QFPGSOTZNXVAU3ID","created_at":"2026-07-05T03:25:25.682383+00:00"},{"alias_kind":"pith_short_8","alias_value":"QFPGSOTZ","created_at":"2026-07-05T03:25:25.682383+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/QFPGSOTZNXVAU3ID7OBTIGEHXB","json":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB.json","graph_json":"https://pith.science/api/pith-number/QFPGSOTZNXVAU3ID7OBTIGEHXB/graph.json","events_json":"https://pith.science/api/pith-number/QFPGSOTZNXVAU3ID7OBTIGEHXB/events.json","paper":"https://pith.science/paper/QFPGSOTZ"},"agent_actions":{"view_html":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB","download_json":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB.json","view_paper":"https://pith.science/paper/QFPGSOTZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.12950&json=true","fetch_graph":"https://pith.science/api/pith-number/QFPGSOTZNXVAU3ID7OBTIGEHXB/graph.json","fetch_events":"https://pith.science/api/pith-number/QFPGSOTZNXVAU3ID7OBTIGEHXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB/action/storage_attestation","attest_author":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB/action/author_attestation","sign_citation":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB/action/citation_signature","submit_replication":"https://pith.science/pith/QFPGSOTZNXVAU3ID7OBTIGEHXB/action/replication_record"}},"created_at":"2026-07-05T03:25:25.682383+00:00","updated_at":"2026-07-05T03:25:25.682383+00:00"}