{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3F7ZSGOVIMTQM3E2OX5TDOBCOY","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":"43136642d3683174bee0e29d6cba83f1d24d04aa06063bdbe1686a2e370a24c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-05-28T15:49:51Z","title_canon_sha256":"c3a60a402a8e57d4c230d21bf17411d41113780723024bc88952b155957dcb7f"},"schema_version":"1.0","source":{"id":"1305.6542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6542","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6542v1","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6542","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"3F7ZSGOVIMTQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3F7ZSGOVIMTQM3E2","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3F7ZSGOV","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:6b7d7f617bbd9d883ce0af2f73130fa8f6d9d293f809b3c39b4a74891e406dc9","target":"graph","created_at":"2026-05-18T03:24:40Z","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":"In this paper we will show that two surfaces of the same genus and homology class in a simply connected 4-manifold are concordant. We will show they are often topologically isotopic when their complements have cyclic fundamental group. Finally, we will show that if they are 0-concordant, then surgery on one is equivalent to surgery on the other.","authors_text":"Nathan Sunukjian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-05-28T15:49:51Z","title":"Surfaces in 4-manifolds: Concordance, Isotopy, and Surgery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6542","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":"sha256:5ab33af8a3474e7dc1b0f574078d528d1f800a8af70b77f20e0a32728930887a","target":"record","created_at":"2026-05-18T03:24:40Z","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":"43136642d3683174bee0e29d6cba83f1d24d04aa06063bdbe1686a2e370a24c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-05-28T15:49:51Z","title_canon_sha256":"c3a60a402a8e57d4c230d21bf17411d41113780723024bc88952b155957dcb7f"},"schema_version":"1.0","source":{"id":"1305.6542","kind":"arxiv","version":1}},"canonical_sha256":"d97f9919d54327066c9a75fb31b82276211519bd5b1c6601aa55c85b5c7264c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d97f9919d54327066c9a75fb31b82276211519bd5b1c6601aa55c85b5c7264c3","first_computed_at":"2026-05-18T03:24:40.493909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:40.493909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QX/C6rqPjr87kcON9KPG3MTVIkhnexyKb9QPyQl8q4lemwnQL++V8NEaivTplQbt3+v6o+PWwF0qp3273R34DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:40.494542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab33af8a3474e7dc1b0f574078d528d1f800a8af70b77f20e0a32728930887a","sha256:6b7d7f617bbd9d883ce0af2f73130fa8f6d9d293f809b3c39b4a74891e406dc9"],"state_sha256":"4462267c854a1093816709aeeaedfd903c80ddda89c0df3b2ec4c9179b0d7101"}