{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:Z6DVWNNFEKAXGX6ZYWJMCQZRTN","short_pith_number":"pith:Z6DVWNNF","schema_version":"1.0","canonical_sha256":"cf875b35a52281735fd9c592c143319b7146bff4a02913b4c437b18764ff0803","source":{"kind":"arxiv","id":"1211.2431","version":2},"attestation_state":"computed","paper":{"title":"Nongeneric J-holomorphic curves in symplectic 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dusa McDuff","submitted_at":"2012-11-11T15:52:30Z","abstract_excerpt":"This note discusses the structure of J-holomorphic curves in symplectic 4-manifolds (M,\\om) when J\\in \\Jj(\\Ss), the set of \\om-tame J for which a fixed chain \\Ss of transversally intersecting embedded spheres of self-intersection \\le -2 is J-holomorphic. Extending work by Biran (in Invent. Math. (1999)), it shows that when (M,\\om) is the blow up of a rational or ruled symplectic 4-manifold, any homology class A\\in H_2(M;\\Z), with nonzero Gromov invariant and nonnegative intersection both with the spheres in \\Ss and with the exceptional classes other than A, has an embedded J-holomorphic repres"},"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":"1211.2431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-11-11T15:52:30Z","cross_cats_sorted":[],"title_canon_sha256":"94758ce113724ae8af113adb65d999fd96068f3d278df994513713bc9a853e62","abstract_canon_sha256":"885d6a3e8772fcfd9dbcc004c4b340c8d1d3fdc057233a66bb582be718ca6a21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:42.707558Z","signature_b64":"E0ZAnRpy+YW275nHukknwpXH+thdg0KH+lSdbgmQEJgnVt8AXBQSim1qL6Xr0KemTwcjoLoCx/ahsD2/frt3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf875b35a52281735fd9c592c143319b7146bff4a02913b4c437b18764ff0803","last_reissued_at":"2026-05-18T03:26:42.706877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:42.706877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nongeneric J-holomorphic curves in symplectic 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dusa McDuff","submitted_at":"2012-11-11T15:52:30Z","abstract_excerpt":"This note discusses the structure of J-holomorphic curves in symplectic 4-manifolds (M,\\om) when J\\in \\Jj(\\Ss), the set of \\om-tame J for which a fixed chain \\Ss of transversally intersecting embedded spheres of self-intersection \\le -2 is J-holomorphic. Extending work by Biran (in Invent. Math. (1999)), it shows that when (M,\\om) is the blow up of a rational or ruled symplectic 4-manifold, any homology class A\\in H_2(M;\\Z), with nonzero Gromov invariant and nonnegative intersection both with the spheres in \\Ss and with the exceptional classes other than A, has an embedded J-holomorphic repres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2431","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":"1211.2431","created_at":"2026-05-18T03:26:42.706971+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2431v2","created_at":"2026-05-18T03:26:42.706971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2431","created_at":"2026-05-18T03:26:42.706971+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z6DVWNNFEKAX","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z6DVWNNFEKAXGX6Z","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z6DVWNNF","created_at":"2026-05-18T12:27:30.460161+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/Z6DVWNNFEKAXGX6ZYWJMCQZRTN","json":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN.json","graph_json":"https://pith.science/api/pith-number/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/graph.json","events_json":"https://pith.science/api/pith-number/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/events.json","paper":"https://pith.science/paper/Z6DVWNNF"},"agent_actions":{"view_html":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN","download_json":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN.json","view_paper":"https://pith.science/paper/Z6DVWNNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2431&json=true","fetch_graph":"https://pith.science/api/pith-number/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/graph.json","fetch_events":"https://pith.science/api/pith-number/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/action/storage_attestation","attest_author":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/action/author_attestation","sign_citation":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/action/citation_signature","submit_replication":"https://pith.science/pith/Z6DVWNNFEKAXGX6ZYWJMCQZRTN/action/replication_record"}},"created_at":"2026-05-18T03:26:42.706971+00:00","updated_at":"2026-05-18T03:26:42.706971+00:00"}