{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KHFO7A6VDIUWYBBDNMYPIKSQCK","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":"4dbe4626597ca7c3e0ea1838a177cdfa67f0d1fa7f62541e39410c0783100f53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-02-02T18:05:48Z","title_canon_sha256":"5a76a82dd1f9e705b1157486bb8c5ae73bfdd250bff310e05ec8ee6e9aa015e4"},"schema_version":"1.0","source":{"id":"1802.00790","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00790","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00790v2","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00790","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"KHFO7A6VDIUW","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KHFO7A6VDIUWYBBD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KHFO7A6V","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:5977a486b67b08e5c5b976c3e78b1e767912856d35cabfb422b57429caf659da","target":"graph","created_at":"2026-05-17T23:52:18Z","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"},"paper":{"abstract_excerpt":"We classify four-dimensional manifolds endowed with symplectic pairs admitting embedded symplectic spheres with non-negative self-intersection, following the strategy of McDuff's classification of rational and ruled symplectic four manifolds.","authors_text":"Gianluca Bande, Paolo Ghiggini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-02-02T18:05:48Z","title":"Holomorphic spheres and four-dimensional symplectic pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00790","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":"sha256:5c67fa0a79bff42669f9043beff24d275be0fdfad4d23b9fda3fc3232e16ea50","target":"record","created_at":"2026-05-17T23:52:18Z","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":"4dbe4626597ca7c3e0ea1838a177cdfa67f0d1fa7f62541e39410c0783100f53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-02-02T18:05:48Z","title_canon_sha256":"5a76a82dd1f9e705b1157486bb8c5ae73bfdd250bff310e05ec8ee6e9aa015e4"},"schema_version":"1.0","source":{"id":"1802.00790","kind":"arxiv","version":2}},"canonical_sha256":"51caef83d51a296c04236b30f42a5012b4f69c115452bea690d444ca33bb2a00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51caef83d51a296c04236b30f42a5012b4f69c115452bea690d444ca33bb2a00","first_computed_at":"2026-05-17T23:52:18.609365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:18.609365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EHmd8k4jwKjH+6ue2kb+emZxx7tbS3nkST8FBcmJdFo9LlyuyxmtY90CaOt1mREhfGLxy3j3aENX0zhUI2QcBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:18.610070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00790","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c67fa0a79bff42669f9043beff24d275be0fdfad4d23b9fda3fc3232e16ea50","sha256:5977a486b67b08e5c5b976c3e78b1e767912856d35cabfb422b57429caf659da"],"state_sha256":"df4b95f98c6000503260fd647aecb3b1bd4415b755dba8220568d54db4974ee3"}