{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2I7KDJ5J5WOUIL6JBPJK6KQA2F","short_pith_number":"pith:2I7KDJ5J","schema_version":"1.0","canonical_sha256":"d23ea1a7a9ed9d442fc90bd2af2a00d141daf97ac6cbeaed9311bd93977adc8c","source":{"kind":"arxiv","id":"1808.09356","version":2},"attestation_state":"computed","paper":{"title":"$J$-holomorphic curves from closed $J$-anti-invariant forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Louis Bonthrone, Weiyi Zhang","submitted_at":"2018-08-28T15:26:17Z","abstract_excerpt":"We study the relation between $J$-anti-invariant $2$-forms and pseudoholomorphic curves in this paper. We show the zero set of a closed $J$-anti-invariant $2$-form on an almost complex $4$-manifold supports a $J$-holomorphic subvariety in the canonical class. This confirms a conjecture of Draghici-Li-Zhang. A higher dimensional analogue is established. We also show the dimension of closed $J$-anti-invariant $2$-forms on an almost complex $4$-manifold is a birational invariant, in the sense that it is invariant under degree one pseudoholomorphic maps."},"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":"1808.09356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-28T15:26:17Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"97f75327adbcddf1070a609399662e24c5e3c5121862bbbf20f9f2e33d148a1e","abstract_canon_sha256":"4efa6645aee9aab2d75a17685cfcee88b98b95b52c0b266f745a8eb16828aa5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:23:53.008515Z","signature_b64":"5H/L4Ia4Yp1rBD+rQo8M61ebxN809d9aMOLkXdA6chN09hE6GvijSaqFTFwPUBIdkpYRawV1fKqfdTR253+rCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d23ea1a7a9ed9d442fc90bd2af2a00d141daf97ac6cbeaed9311bd93977adc8c","last_reissued_at":"2026-07-05T01:23:53.008150Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:23:53.008150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$J$-holomorphic curves from closed $J$-anti-invariant forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Louis Bonthrone, Weiyi Zhang","submitted_at":"2018-08-28T15:26:17Z","abstract_excerpt":"We study the relation between $J$-anti-invariant $2$-forms and pseudoholomorphic curves in this paper. We show the zero set of a closed $J$-anti-invariant $2$-form on an almost complex $4$-manifold supports a $J$-holomorphic subvariety in the canonical class. This confirms a conjecture of Draghici-Li-Zhang. A higher dimensional analogue is established. We also show the dimension of closed $J$-anti-invariant $2$-forms on an almost complex $4$-manifold is a birational invariant, in the sense that it is invariant under degree one pseudoholomorphic maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09356","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.09356/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":"1808.09356","created_at":"2026-07-05T01:23:53.008213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.09356v2","created_at":"2026-07-05T01:23:53.008213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09356","created_at":"2026-07-05T01:23:53.008213+00:00"},{"alias_kind":"pith_short_12","alias_value":"2I7KDJ5J5WOU","created_at":"2026-07-05T01:23:53.008213+00:00"},{"alias_kind":"pith_short_16","alias_value":"2I7KDJ5J5WOUIL6J","created_at":"2026-07-05T01:23:53.008213+00:00"},{"alias_kind":"pith_short_8","alias_value":"2I7KDJ5J","created_at":"2026-07-05T01:23:53.008213+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.03016","citing_title":"On the Anti-Invariant Cohomology of Almost Complex Manifolds","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F","json":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F.json","graph_json":"https://pith.science/api/pith-number/2I7KDJ5J5WOUIL6JBPJK6KQA2F/graph.json","events_json":"https://pith.science/api/pith-number/2I7KDJ5J5WOUIL6JBPJK6KQA2F/events.json","paper":"https://pith.science/paper/2I7KDJ5J"},"agent_actions":{"view_html":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F","download_json":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F.json","view_paper":"https://pith.science/paper/2I7KDJ5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.09356&json=true","fetch_graph":"https://pith.science/api/pith-number/2I7KDJ5J5WOUIL6JBPJK6KQA2F/graph.json","fetch_events":"https://pith.science/api/pith-number/2I7KDJ5J5WOUIL6JBPJK6KQA2F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F/action/storage_attestation","attest_author":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F/action/author_attestation","sign_citation":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F/action/citation_signature","submit_replication":"https://pith.science/pith/2I7KDJ5J5WOUIL6JBPJK6KQA2F/action/replication_record"}},"created_at":"2026-07-05T01:23:53.008213+00:00","updated_at":"2026-07-05T01:23:53.008213+00:00"}