{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LAAFJB25JQESN7HEFSKUBRB4FV","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":"a7cec486998c5dee91f3d7092227de02e352d5b068f50d42894fd965bbfced57","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-27T13:00:58Z","title_canon_sha256":"26215bd306e7f0abebffd522146dccd110d9fa054f00add27e8e98839be052e5"},"schema_version":"1.0","source":{"id":"1308.5853","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5853","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5853v2","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5853","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"LAAFJB25JQES","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LAAFJB25JQESN7HE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LAAFJB25","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:1b3e80aeae9db18e259074280634f2d39aaa7c85b27f66fefae845e6bdc58c7b","target":"graph","created_at":"2026-05-18T03:09:47Z","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":"A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is hyperfinite. In this paper we show that this question has a positive answer when the acting group is locally nilpotent. This extends previous results obtained by Gao-Jackson for abelian groups and by Jackson-Kechris-Louveau for finitely generated nilpotent-by-finite groups. Our proof is based on a mixture of coarse geometric properties of locally nilpotent groups together with an adaptation of the Gao-Jackson machine","authors_text":"Brandon Seward, Scott Schneider","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-27T13:00:58Z","title":"Locally Nilpotent Groups and Hyperfinite Equivalence Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5853","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:b8b5210ed25b1d7660073973bbd745f21e99f49dddbec64cbbf1569d65364d60","target":"record","created_at":"2026-05-18T03:09:47Z","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":"a7cec486998c5dee91f3d7092227de02e352d5b068f50d42894fd965bbfced57","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-27T13:00:58Z","title_canon_sha256":"26215bd306e7f0abebffd522146dccd110d9fa054f00add27e8e98839be052e5"},"schema_version":"1.0","source":{"id":"1308.5853","kind":"arxiv","version":2}},"canonical_sha256":"580054875d4c0926fce42c9540c43c2d4acdc1729e8c9bdd2671ea8b1debeb9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"580054875d4c0926fce42c9540c43c2d4acdc1729e8c9bdd2671ea8b1debeb9e","first_computed_at":"2026-05-18T03:09:47.771109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:47.771109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ojXPhZqTES3WNYgXVMPMaaOALSzZO0kR4VPHkagDfWSz0/Tj49AeD5lmzLADfMLAiOla0+7VVaNpgMq4YcTqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:47.771936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5853","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8b5210ed25b1d7660073973bbd745f21e99f49dddbec64cbbf1569d65364d60","sha256:1b3e80aeae9db18e259074280634f2d39aaa7c85b27f66fefae845e6bdc58c7b"],"state_sha256":"e96d668f4c0899a8cfab9d2de7e128444f23e385d3c461b8ce129fbeb5cc37de"}