{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N7WWMUBDVHCFMODSVETLAVCT6N","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":"e5cf53126fad4759828735eb44a9644f3559777d9255000c6b58ff9d78b40c49","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-11T12:59:45Z","title_canon_sha256":"55f7fbd9fa95151416a2023bff24b1c4dda3d6ff1bd710b6831c8fabdf5df716"},"schema_version":"1.0","source":{"id":"1312.3149","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3149","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3149v3","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3149","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"N7WWMUBDVHCF","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N7WWMUBDVHCFMODS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N7WWMUBD","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:ba301650a92237ce19fb3c10e809bf33b5da870d3b20c4ee256b6d3b7c933090","target":"graph","created_at":"2026-05-18T01:34:42Z","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":"We prove that if $X$ is a compact, oriented, connected $4$-dimensional smooth manifold, possibly with boundary, satisfying $\\chi(X)\\neq 0$, then there exists an integer $C\\geq 1$ such that any finite group $G$ acting smoothly and effectively on $X$ has an abelian subgroup $A$ satisfying $[G:A]\\leq C$, $\\chi(X^A)=\\chi(X)$, and $A$ can be generated by at most $2$ elements. Furthermore, if $\\chi(X)<0$ then $A$ is cyclic. This proves, for any such $X$, a conjecture of Ghys. We also prove an analogous result for manifolds of arbitrary dimension and non-vanishing Euler characteristic, but restricted","authors_text":"Ignasi Mundet i Riera","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-11T12:59:45Z","title":"Finite group actions on 4-manifolds with nonzero Euler characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3149","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":"sha256:80e40b3d4fe2b793268b4a7223de2bb0c19d20382b0eadf440f7f34b5b08b1ff","target":"record","created_at":"2026-05-18T01:34:42Z","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":"e5cf53126fad4759828735eb44a9644f3559777d9255000c6b58ff9d78b40c49","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-11T12:59:45Z","title_canon_sha256":"55f7fbd9fa95151416a2023bff24b1c4dda3d6ff1bd710b6831c8fabdf5df716"},"schema_version":"1.0","source":{"id":"1312.3149","kind":"arxiv","version":3}},"canonical_sha256":"6fed665023a9c4563872a926b05453f3584b1efaeb06c02f08d49ce746306529","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fed665023a9c4563872a926b05453f3584b1efaeb06c02f08d49ce746306529","first_computed_at":"2026-05-18T01:34:42.337630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:42.337630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xyGf+POEAuLZL1Shocj/vX9LbEClLEvzAXzOp1UKa8kW5UJd/Y2EHqge72XUAs5sTk0xuPOHEr4M5CfIQRyVDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:42.338195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3149","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80e40b3d4fe2b793268b4a7223de2bb0c19d20382b0eadf440f7f34b5b08b1ff","sha256:ba301650a92237ce19fb3c10e809bf33b5da870d3b20c4ee256b6d3b7c933090"],"state_sha256":"0b5ee07381a0e98197cd6ab09b46cbb7357c3db0e83dc40c792431eda6ea01d5"}