{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:FYG4Z2GXFO67RIS27QCIXHZO5W","short_pith_number":"pith:FYG4Z2GX","schema_version":"1.0","canonical_sha256":"2e0dcce8d72bbdf8a25afc048b9f2eed9c50e3302c3644d39a87c223400a93f7","source":{"kind":"arxiv","id":"0905.4049","version":3},"attestation_state":"computed","paper":{"title":"Hamiltonian circle actions with minimal fixed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Hui Li, Susan Tolman","submitted_at":"2009-05-25T18:23:57Z","abstract_excerpt":"Consider an effective Hamiltonian circle action on a compact symplectic $2n$-dimensional manifold $(M, \\omega)$. Assume that the fixed set $M^{S^1}$ is {\\em minimal}, in two senses: it has exactly two components, $X$ and $Y$, and $\\dim(X) + \\dim(Y) = \\dim(M) - 2$.\n  We prove that the integral cohomology ring and Chern classes of $M$ are isomorphic to either those of $\\CP^n$ or (if $n \\neq 1$ is odd) to those of $\\Gt_2(\\R^{n+2})$, the Grassmannian of oriented two-planes in $\\R^{n+2}$. In particular, $H^i(M;\\Z) = H^i(\\CP^n;\\Z)$ for all $i$, and the Chern classes of $M$ are determined by the inte"},"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":"0905.4049","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-05-25T18:23:57Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f22b7919cd4906c28c69adaf63a9e2a26fc5af8b27babc76c92b5444c267d937","abstract_canon_sha256":"44e1dbbcbd1c1c1fd1394e71a1e6f81986bdff2dcff494d26edf31228aae0a4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:42.253426Z","signature_b64":"CutzM3pRBul5QnnXd7UkRcdmgXf4zIZmB7dcarZV/u/59Y9uD8OGv5t7U9U3FmkRZd5YVC8Z+A/Y1oqMi+4bDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e0dcce8d72bbdf8a25afc048b9f2eed9c50e3302c3644d39a87c223400a93f7","last_reissued_at":"2026-05-18T03:24:42.252784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:42.252784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian circle actions with minimal fixed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Hui Li, Susan Tolman","submitted_at":"2009-05-25T18:23:57Z","abstract_excerpt":"Consider an effective Hamiltonian circle action on a compact symplectic $2n$-dimensional manifold $(M, \\omega)$. Assume that the fixed set $M^{S^1}$ is {\\em minimal}, in two senses: it has exactly two components, $X$ and $Y$, and $\\dim(X) + \\dim(Y) = \\dim(M) - 2$.\n  We prove that the integral cohomology ring and Chern classes of $M$ are isomorphic to either those of $\\CP^n$ or (if $n \\neq 1$ is odd) to those of $\\Gt_2(\\R^{n+2})$, the Grassmannian of oriented two-planes in $\\R^{n+2}$. In particular, $H^i(M;\\Z) = H^i(\\CP^n;\\Z)$ for all $i$, and the Chern classes of $M$ are determined by the inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4049","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":"0905.4049","created_at":"2026-05-18T03:24:42.252884+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.4049v3","created_at":"2026-05-18T03:24:42.252884+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4049","created_at":"2026-05-18T03:24:42.252884+00:00"},{"alias_kind":"pith_short_12","alias_value":"FYG4Z2GXFO67","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"FYG4Z2GXFO67RIS2","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"FYG4Z2GX","created_at":"2026-05-18T12:25:59.703012+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/FYG4Z2GXFO67RIS27QCIXHZO5W","json":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W.json","graph_json":"https://pith.science/api/pith-number/FYG4Z2GXFO67RIS27QCIXHZO5W/graph.json","events_json":"https://pith.science/api/pith-number/FYG4Z2GXFO67RIS27QCIXHZO5W/events.json","paper":"https://pith.science/paper/FYG4Z2GX"},"agent_actions":{"view_html":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W","download_json":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W.json","view_paper":"https://pith.science/paper/FYG4Z2GX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.4049&json=true","fetch_graph":"https://pith.science/api/pith-number/FYG4Z2GXFO67RIS27QCIXHZO5W/graph.json","fetch_events":"https://pith.science/api/pith-number/FYG4Z2GXFO67RIS27QCIXHZO5W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W/action/storage_attestation","attest_author":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W/action/author_attestation","sign_citation":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W/action/citation_signature","submit_replication":"https://pith.science/pith/FYG4Z2GXFO67RIS27QCIXHZO5W/action/replication_record"}},"created_at":"2026-05-18T03:24:42.252884+00:00","updated_at":"2026-05-18T03:24:42.252884+00:00"}