{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6L4ZU7HBH5E6UC4FYDJ6CD63GJ","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":"9f64598ad83ae0707269a7ffa6e735e49c4741b18291bf3e57731f90b2cd5535","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-11T18:23:48Z","title_canon_sha256":"3502a253576d56692b36253b14ebc577bf99b8af5bb5d3caddba9d42ef74c740"},"schema_version":"1.0","source":{"id":"1406.2986","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2986","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2986v3","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2986","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"6L4ZU7HBH5E6","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6L4ZU7HBH5E6UC4F","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6L4ZU7HB","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:203647fdf9a199996d3511aea443c4a67cf8648b45b7b61a69378f6842142016","target":"graph","created_at":"2026-05-17T23:52:19Z","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 note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is given by one half of the Euler characteristic of the 4-manifold. The result also shows that in some cases the 4-manifold does not admit such actions of a certain order at all or that any such action has to be pseudofree.","authors_text":"M. J. D. Hamilton","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-11T18:23:48Z","title":"Cyclic group actions and embedded spheres in 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2986","kind":"arxiv","version":3},"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":"sha256:3cb1e5d38e705ce65ca6059245611ac2caf894490b9ed91a1e061b245f07f62f","target":"record","created_at":"2026-05-17T23:52:19Z","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":"9f64598ad83ae0707269a7ffa6e735e49c4741b18291bf3e57731f90b2cd5535","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-11T18:23:48Z","title_canon_sha256":"3502a253576d56692b36253b14ebc577bf99b8af5bb5d3caddba9d42ef74c740"},"schema_version":"1.0","source":{"id":"1406.2986","kind":"arxiv","version":3}},"canonical_sha256":"f2f99a7ce13f49ea0b85c0d3e10fdb326f5ddffe64b9f3476eb6ef50615a2f7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2f99a7ce13f49ea0b85c0d3e10fdb326f5ddffe64b9f3476eb6ef50615a2f7f","first_computed_at":"2026-05-17T23:52:19.421805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:19.421805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7SgMU9LD1BhnIARiOQ+7E4T1B7zbumFsl3B6LYupEqvUNHKhFphqji4CPTeQlDIJnlUCKiDYm9IUBR2R0iThAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:19.422586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2986","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cb1e5d38e705ce65ca6059245611ac2caf894490b9ed91a1e061b245f07f62f","sha256:203647fdf9a199996d3511aea443c4a67cf8648b45b7b61a69378f6842142016"],"state_sha256":"ccd31b5d9f4f700dec2408fecd4202192a4b6fe563b7004681d69b36590764e4"}