{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XSWDIJ2FW7BIEJVPUFKP3CUSHT","short_pith_number":"pith:XSWDIJ2F","schema_version":"1.0","canonical_sha256":"bcac342745b7c28226afa154fd8a923cd16788d012ebed5d675fe9b1b209e2ae","source":{"kind":"arxiv","id":"1007.3281","version":3},"attestation_state":"computed","paper":{"title":"Altering symplectic manifolds by homologous recombination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Mohammed Abouzaid, Paul Seidel","submitted_at":"2010-07-19T20:52:01Z","abstract_excerpt":"We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a method, which we call homologous recombination, for constructing a Lefschetz fibration whose total space is smoothly equivalent to the original variety, but for which symplectic cohomology with coefficients in the given set of primes vanishes (there is also a simpler version that kills symplectic cohomology completely). Rather than relying on a geometric ana"},"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":"1007.3281","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-07-19T20:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"fe516979205001eb6c17a74c042f37e4c54daa1bae1554bd1e9d6a3e22767ed5","abstract_canon_sha256":"b2c9cb2103d3d27cc70120a4fa82f4c458c64d74142b033869d57b1d944e9826"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:43.127297Z","signature_b64":"RazcsOIB91KFCpIw3pT/FmK2ruAnCMbSgCET3SCJaYnNQ5qjFePpQvdi+1LfthbBU7OtsxIDCnZQor81K6RXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcac342745b7c28226afa154fd8a923cd16788d012ebed5d675fe9b1b209e2ae","last_reissued_at":"2026-05-18T04:42:43.126863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:43.126863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Altering symplectic manifolds by homologous recombination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Mohammed Abouzaid, Paul Seidel","submitted_at":"2010-07-19T20:52:01Z","abstract_excerpt":"We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a method, which we call homologous recombination, for constructing a Lefschetz fibration whose total space is smoothly equivalent to the original variety, but for which symplectic cohomology with coefficients in the given set of primes vanishes (there is also a simpler version that kills symplectic cohomology completely). Rather than relying on a geometric ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3281","kind":"arxiv","version":3},"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":"1007.3281","created_at":"2026-05-18T04:42:43.126930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.3281v3","created_at":"2026-05-18T04:42:43.126930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3281","created_at":"2026-05-18T04:42:43.126930+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSWDIJ2FW7BI","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSWDIJ2FW7BIEJVP","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSWDIJ2F","created_at":"2026-05-18T12:26:17.028572+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/XSWDIJ2FW7BIEJVPUFKP3CUSHT","json":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT.json","graph_json":"https://pith.science/api/pith-number/XSWDIJ2FW7BIEJVPUFKP3CUSHT/graph.json","events_json":"https://pith.science/api/pith-number/XSWDIJ2FW7BIEJVPUFKP3CUSHT/events.json","paper":"https://pith.science/paper/XSWDIJ2F"},"agent_actions":{"view_html":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT","download_json":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT.json","view_paper":"https://pith.science/paper/XSWDIJ2F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.3281&json=true","fetch_graph":"https://pith.science/api/pith-number/XSWDIJ2FW7BIEJVPUFKP3CUSHT/graph.json","fetch_events":"https://pith.science/api/pith-number/XSWDIJ2FW7BIEJVPUFKP3CUSHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT/action/storage_attestation","attest_author":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT/action/author_attestation","sign_citation":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT/action/citation_signature","submit_replication":"https://pith.science/pith/XSWDIJ2FW7BIEJVPUFKP3CUSHT/action/replication_record"}},"created_at":"2026-05-18T04:42:43.126930+00:00","updated_at":"2026-05-18T04:42:43.126930+00:00"}