{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YFZUPZ7FKVHX3NDKJWV57WCJSC","short_pith_number":"pith:YFZUPZ7F","schema_version":"1.0","canonical_sha256":"c17347e7e5554f7db46a4dabdfd84990b1c5467aa665a55aaabe0038235e6c3c","source":{"kind":"arxiv","id":"1507.05972","version":3},"attestation_state":"computed","paper":{"title":"Circle actions on symplectic four-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Liat Kessler, Tara S. Holm","submitted_at":"2015-07-21T20:06:41Z","abstract_excerpt":"We complete the classification of Hamiltonian torus and circle actions on symplectic four-dimensional manifolds. Following work of Delzant and Karshon, Hamiltonian circle and 2-torus actions on any fixed simply connected symplectic four-manifold were characterized by Karshon, Kessler and Pinsonnault. What remains is to study the case of Hamiltonian actions on blowups of S^2-bundles over a Riemann surface of positive genus. These do not admit 2-torus actions. In this paper, we characterize Hamiltonian circle actions on them. We then derive combinatorial results on the existence and counting of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.05972","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-07-21T20:06:41Z","cross_cats_sorted":[],"title_canon_sha256":"9d4a8721f1b99873c82c950faaaa95ad7b4512fa6f53d04c2569163b6f2eea41","abstract_canon_sha256":"14b92e3f0eeefde7d28dea185da2a5de17504e091b4f0bf35b05a8a2ea890598"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:55.589828Z","signature_b64":"RudEVuBUMxUYOp5B36B0JckrQXWICxhswVM1oYBUTdWn7Au4qSa/pOu2cAAFGqpBn16Nzd9qMD9qS+3L9tGpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c17347e7e5554f7db46a4dabdfd84990b1c5467aa665a55aaabe0038235e6c3c","last_reissued_at":"2026-05-18T00:52:55.589390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:55.589390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Circle actions on symplectic four-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Liat Kessler, Tara S. Holm","submitted_at":"2015-07-21T20:06:41Z","abstract_excerpt":"We complete the classification of Hamiltonian torus and circle actions on symplectic four-dimensional manifolds. Following work of Delzant and Karshon, Hamiltonian circle and 2-torus actions on any fixed simply connected symplectic four-manifold were characterized by Karshon, Kessler and Pinsonnault. What remains is to study the case of Hamiltonian actions on blowups of S^2-bundles over a Riemann surface of positive genus. These do not admit 2-torus actions. In this paper, we characterize Hamiltonian circle actions on them. We then derive combinatorial results on the existence and counting of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05972","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.05972","created_at":"2026-05-18T00:52:55.589460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05972v3","created_at":"2026-05-18T00:52:55.589460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05972","created_at":"2026-05-18T00:52:55.589460+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFZUPZ7FKVHX","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFZUPZ7FKVHX3NDK","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFZUPZ7F","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC","json":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC.json","graph_json":"https://pith.science/api/pith-number/YFZUPZ7FKVHX3NDKJWV57WCJSC/graph.json","events_json":"https://pith.science/api/pith-number/YFZUPZ7FKVHX3NDKJWV57WCJSC/events.json","paper":"https://pith.science/paper/YFZUPZ7F"},"agent_actions":{"view_html":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC","download_json":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC.json","view_paper":"https://pith.science/paper/YFZUPZ7F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05972&json=true","fetch_graph":"https://pith.science/api/pith-number/YFZUPZ7FKVHX3NDKJWV57WCJSC/graph.json","fetch_events":"https://pith.science/api/pith-number/YFZUPZ7FKVHX3NDKJWV57WCJSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC/action/storage_attestation","attest_author":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC/action/author_attestation","sign_citation":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC/action/citation_signature","submit_replication":"https://pith.science/pith/YFZUPZ7FKVHX3NDKJWV57WCJSC/action/replication_record"}},"created_at":"2026-05-18T00:52:55.589460+00:00","updated_at":"2026-05-18T00:52:55.589460+00:00"}