{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L7Z63WGKONZLUX4E34RETJMIAH","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":"81b32e2880becc359bedb7d0b60c4523cf1147cf1a9377bde9ea4442e16f879c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-08-27T22:16:47Z","title_canon_sha256":"42373f1bb6bcd0c4e5ec495b9ae31893e228ef5ce7cf2340361c1e7de4619443"},"schema_version":"1.0","source":{"id":"1408.6580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6580","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6580v2","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6580","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"L7Z63WGKONZL","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L7Z63WGKONZLUX4E","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L7Z63WGK","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:1849b44330b9ec67be9ef5cded711a0b3f7c24686825f3a5cc3665139b4ce825","target":"graph","created_at":"2026-05-18T00:38:36Z","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":"Consider a Hamiltonian circle action on a closed $8$-dimensional symplectic manifold $M$ with exactly five fixed points, which is the smallest possible fixed set. In their paper, L. Godinho and S. Sabatini show that if $M$ satisfies an extra \"positivity condition\" then the isotropy weights at the fixed points of $M$ agree with those of some linear action on $\\mathbb{CP}^4$. Therefore, the (equivariant) cohomology rings and the (equivariant) Chern classes of $M$ and $\\mathbb{CP}^4$ agree; in particular, $H^*(M;\\mathbb{Z}) \\simeq \\mathbb{Z}[y]/y^5$ and $c(TM) = (1+y)^5$. In this paper, we prove ","authors_text":"Donghoon Jang, Susan Tolman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-08-27T22:16:47Z","title":"Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6580","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":"sha256:6f1aba858bac9a3f1eae314dde43407d0bdd32438d87fdd408d714a02263fe18","target":"record","created_at":"2026-05-18T00:38:36Z","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":"81b32e2880becc359bedb7d0b60c4523cf1147cf1a9377bde9ea4442e16f879c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-08-27T22:16:47Z","title_canon_sha256":"42373f1bb6bcd0c4e5ec495b9ae31893e228ef5ce7cf2340361c1e7de4619443"},"schema_version":"1.0","source":{"id":"1408.6580","kind":"arxiv","version":2}},"canonical_sha256":"5ff3edd8ca7372ba5f84df2249a58801e2f2b690442fa79672185373fa8317d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ff3edd8ca7372ba5f84df2249a58801e2f2b690442fa79672185373fa8317d6","first_computed_at":"2026-05-18T00:38:36.811929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:36.811929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pneeOoMC3BykeY9UnNuiESKYxiS5+p/PEWfLJF35eQmzfn9fLQrsn+m4Jrd00D+DRf/HVFG02XwBw/vJfcZFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:36.812420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f1aba858bac9a3f1eae314dde43407d0bdd32438d87fdd408d714a02263fe18","sha256:1849b44330b9ec67be9ef5cded711a0b3f7c24686825f3a5cc3665139b4ce825"],"state_sha256":"5a3d851c294efeda13eeb9fecace4e6c2de26488fd6e8407ef1b79da94e8547b"}