{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:RBHPYW7P5PTXN6VMSV7XK3ZRFI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dc66207e291abc056bfb65a651404b084f5661c2e3547e526ffd0625d8e342fc","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2001-07-29T16:46:00Z","title_canon_sha256":"dd34428bc7be5b144e5b13da1f6dd5ef24cde4b9c7e763a9520b8eebbd87e9ff"},"schema_version":"1.0","source":{"id":"math/0107211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107211","created_at":"2026-07-04T14:35:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107211v2","created_at":"2026-07-04T14:35:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107211","created_at":"2026-07-04T14:35:27Z"},{"alias_kind":"pith_short_12","alias_value":"RBHPYW7P5PTX","created_at":"2026-07-04T14:35:27Z"},{"alias_kind":"pith_short_16","alias_value":"RBHPYW7P5PTXN6VM","created_at":"2026-07-04T14:35:27Z"},{"alias_kind":"pith_short_8","alias_value":"RBHPYW7P","created_at":"2026-07-04T14:35:27Z"}],"graph_snapshots":[{"event_id":"sha256:2b8f968477d60898f9178bd42987fe0dfe82844d1e37fe06057f35c5e12044ca","target":"graph","created_at":"2026-07-04T14:35:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0107211/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber structure plays a more prominent role. We derive some wall crossing formulas measuring how the family Seiberg-Witten invariants change from one chamber to another.","authors_text":"Ai-Ko Liu, Tian-Jun Li","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2001-07-29T16:46:00Z","title":"Family Seiberg-Witten invariants and wall crossing formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107211","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ba71d76600b11b03d0ff4fddd8f16ea0bad4e583efd7a6071536090dbb88521b","target":"record","created_at":"2026-07-04T14:35:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dc66207e291abc056bfb65a651404b084f5661c2e3547e526ffd0625d8e342fc","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2001-07-29T16:46:00Z","title_canon_sha256":"dd34428bc7be5b144e5b13da1f6dd5ef24cde4b9c7e763a9520b8eebbd87e9ff"},"schema_version":"1.0","source":{"id":"math/0107211","kind":"arxiv","version":2}},"canonical_sha256":"884efc5befebe776faac957f756f312a0637ee1fd702d7fb14a2d88d7693decd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"884efc5befebe776faac957f756f312a0637ee1fd702d7fb14a2d88d7693decd","first_computed_at":"2026-07-04T14:35:27.187612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:27.187612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TRGmoyD+w2hjpsjTylVFcxH8YNstMdDf/tOY9sUgUP2innkZMibuvcrS3dJHg6Fh9SesYQK7z0LdTdj9a0J7Cg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:27.188017Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0107211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba71d76600b11b03d0ff4fddd8f16ea0bad4e583efd7a6071536090dbb88521b","sha256:2b8f968477d60898f9178bd42987fe0dfe82844d1e37fe06057f35c5e12044ca"],"state_sha256":"a3de4231569a05c19c51d0c381489125d70fbb96cde3394c1d92d1ebde4f0946"}