{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HL7IU37LELSP7ABKSJESRR5WJB","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":"139d30f88580af11264d5078d9316f191130c1fa17d6f3b8ea230c8038317be6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-03-11T16:48:56Z","title_canon_sha256":"cca75adf60598e05b3d91336a9a8a12d13cdde4ea0ca3f85ce5eb58948a85bec"},"schema_version":"1.0","source":{"id":"1303.2581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2581","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2581v1","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2581","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"HL7IU37LELSP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HL7IU37LELSP7ABK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HL7IU37L","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:787a7a9491fe68d941fb75211f11121d0ef2577bba2a3e02c30d884983defe69","target":"graph","created_at":"2026-05-18T03:31:18Z","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":"Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres $C_n$ is replaced with a rational homology ball $B_n$, $n \\geq 2$. Subsequently, Symington [Sy] defined this procedure in the symplectic category, where a symplectic $C_n$ (given by symplectic spheres) is replaced by a symplectic copy of $B_n$ to yield a new symplectic manifold. As a result, a symplectic rational blow-down can be performed on a manifold whenever such a configuration of symplectic spheres can be found. In this paper, we define the inverse","authors_text":"Tatyana Khodorovskiy","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-03-11T16:48:56Z","title":"Symplectic Rational Blow-up"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2581","kind":"arxiv","version":1},"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":"sha256:415f84d012f2ec9dcd113cba52ac9088544ce2d817161463280be4cf31fe2902","target":"record","created_at":"2026-05-18T03:31:18Z","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":"139d30f88580af11264d5078d9316f191130c1fa17d6f3b8ea230c8038317be6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-03-11T16:48:56Z","title_canon_sha256":"cca75adf60598e05b3d91336a9a8a12d13cdde4ea0ca3f85ce5eb58948a85bec"},"schema_version":"1.0","source":{"id":"1303.2581","kind":"arxiv","version":1}},"canonical_sha256":"3afe8a6feb22e4ff802a924928c7b6487b3559661942edd997befe450b8277da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3afe8a6feb22e4ff802a924928c7b6487b3559661942edd997befe450b8277da","first_computed_at":"2026-05-18T03:31:18.570679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:18.570679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vbiE9VND63IYpTDuogZhjerdzaKaSfzJ6Xv/t2NfF5jcD77DKPQEJExKmZlYxhoBMStOkPAvIo+AKvwhdwPjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:18.571233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:415f84d012f2ec9dcd113cba52ac9088544ce2d817161463280be4cf31fe2902","sha256:787a7a9491fe68d941fb75211f11121d0ef2577bba2a3e02c30d884983defe69"],"state_sha256":"c7aec791abd243da673608c2322e4023d84f660555047721534566f5f41eddb7"}