{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YR6SQOI7XKGZBVLZPMZNF5MUAC","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":"12b3c25a4aad77b4a099bbc0a986d344f10584d6fe53f9aaef8aa6198b01023c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-07-20T15:19:21Z","title_canon_sha256":"706c1d01a5af05bc025db6d7ed4a68d43c6772018d0357028bddf20c39f7de81"},"schema_version":"1.0","source":{"id":"1207.4977","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4977","created_at":"2026-05-18T01:23:31Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4977v2","created_at":"2026-05-18T01:23:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4977","created_at":"2026-05-18T01:23:31Z"},{"alias_kind":"pith_short_12","alias_value":"YR6SQOI7XKGZ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YR6SQOI7XKGZBVLZ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YR6SQOI7","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:ed26531d5e4d685b7bac0f77c80ee13b1662b9d180bc3d08ff180fe73c87e845","target":"graph","created_at":"2026-05-18T01:23:31Z","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":"The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces.\n  More precisely, we will show that (1) if $(M,\\omega)$ admits a Hamiltonian $S^1$-action, then there exists an $S^1$-invariant symplectic $2$-sphere $S$ in $(M,\\omega)$ such that $\\langle c_1(M), [S] \\rangle > 0$, and (2) if the action is non-Hamiltonian, then there exists an $S^1$-invariant symplectic\n  $2$-torus $T$ in $(M,\\omega)$ such that $\\langle c_1(M), [T] \\rangle = 0$.\n  As applications, we will give a very simple proo","authors_text":"Dong Youp Suh, Min Kyu Kim, Yunhyung Cho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-07-20T15:19:21Z","title":"Embedded surfaces for symplectic circle actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4977","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":"sha256:490c1987cf4bc1661bce2503b076a1751c6ee7babc82f1a7b9bdda604d270fab","target":"record","created_at":"2026-05-18T01:23:31Z","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":"12b3c25a4aad77b4a099bbc0a986d344f10584d6fe53f9aaef8aa6198b01023c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-07-20T15:19:21Z","title_canon_sha256":"706c1d01a5af05bc025db6d7ed4a68d43c6772018d0357028bddf20c39f7de81"},"schema_version":"1.0","source":{"id":"1207.4977","kind":"arxiv","version":2}},"canonical_sha256":"c47d28391fba8d90d5797b32d2f594009866200675aaeaae1ffd0b495613a1b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c47d28391fba8d90d5797b32d2f594009866200675aaeaae1ffd0b495613a1b6","first_computed_at":"2026-05-18T01:23:31.746487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:31.746487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rdH7abrtrHBdsFO2NVZU/x//Mb6KZgLBrDemCPvg87JVX/1gLmJdCSH7J/KQQHiKSVp5iW8ZKSm8+Or7jAtFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:31.747048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4977","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:490c1987cf4bc1661bce2503b076a1751c6ee7babc82f1a7b9bdda604d270fab","sha256:ed26531d5e4d685b7bac0f77c80ee13b1662b9d180bc3d08ff180fe73c87e845"],"state_sha256":"0d9f7b9a45984d335828386001d7bd1e33cfc6bb44421fbfa3f445674e54833c"}