{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:22MHLGPV7MWRZIMMSWLSTCUSF7","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":"ddc35857fc73da242f81236e47b47baa75a7d623a045c2d3e6a632e388c1af6b","cross_cats_sorted":["math.DS","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-15T08:54:24Z","title_canon_sha256":"9da7d2f4cdabd85916c14de07050e4912bd8f5f4429f2d9b97ee6fe6b92cd2f9"},"schema_version":"1.0","source":{"id":"1309.3739","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3739","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3739v2","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3739","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"22MHLGPV7MWR","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"22MHLGPV7MWRZIMM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"22MHLGPV","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:c5af0007650b830ced176de79fe9d37960a42d906e8ecc85a1450c9c95dccb48","target":"graph","created_at":"2026-05-18T00:44:10Z","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":"Let us say that a discrete countable group is stable if it has an ergodic, free, probability-measure-preserving and stable action. Let G be a discrete countable group with a central subgroup C. We present a sufficient condition and a necessary condition for G to be stable. We show that if the pair (G, C) does not have property (T), then G is stable. We also show that if the pair (G, C) has property (T) and G is stable, then the quotient group G/C is stable.","authors_text":"Yoshikata Kida","cross_cats":["math.DS","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-15T08:54:24Z","title":"Stable actions of central extensions and relative property (T)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3739","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":"sha256:5896bf13c013c901a4e5cf30341bd38203f73253819be96fc5b56bbd68347283","target":"record","created_at":"2026-05-18T00:44:10Z","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":"ddc35857fc73da242f81236e47b47baa75a7d623a045c2d3e6a632e388c1af6b","cross_cats_sorted":["math.DS","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-15T08:54:24Z","title_canon_sha256":"9da7d2f4cdabd85916c14de07050e4912bd8f5f4429f2d9b97ee6fe6b92cd2f9"},"schema_version":"1.0","source":{"id":"1309.3739","kind":"arxiv","version":2}},"canonical_sha256":"d6987599f5fb2d1ca18c9597298a922fefea4af6aecdd02a06078b687896ecbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6987599f5fb2d1ca18c9597298a922fefea4af6aecdd02a06078b687896ecbf","first_computed_at":"2026-05-18T00:44:10.326507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:10.326507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OvY6J3KNrtngsJrJaMUl4fYjqqXCqVGvfIOnaN9MF9Xl98fzkgmOnvMvuqVMRBCHGJ2HVk1CYpCbyEBZiXKNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:10.326972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3739","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5896bf13c013c901a4e5cf30341bd38203f73253819be96fc5b56bbd68347283","sha256:c5af0007650b830ced176de79fe9d37960a42d906e8ecc85a1450c9c95dccb48"],"state_sha256":"e74dd2770b79b2378821c14b746d413ead24e119896b5025feb9999626f50722"}