{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YJPAVEELPKWERGLV4JJL53JTZD","short_pith_number":"pith:YJPAVEEL","schema_version":"1.0","canonical_sha256":"c25e0a908b7aac489975e252beed33c8ccc82dbe485e54c8770dcc93b405493a","source":{"kind":"arxiv","id":"1307.7539","version":3},"attestation_state":"computed","paper":{"title":"Stabilizer Rigidity in Irreducible Group Actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Omer Tamuz, Yair Hartman","submitted_at":"2013-07-29T11:05:18Z","abstract_excerpt":"We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader-Shalom and Nevo-Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader-Shalom and Stuck-Zimmer."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.7539","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-29T11:05:18Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"7a477e9a7f1438eb62e8142bc4bbd0351cf89af0a40f511bd2f2b058ef25ddfa","abstract_canon_sha256":"610ca4aa1200155bca9161f6094b7d5b9fbb61e04021ce59b31038affb32e379"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:36.348807Z","signature_b64":"1iaP6T/leofv461rnGSSuKxTRdF74L/k5upsNsMziDSQ1KSMLMkXV5MTZwpwvEX3x+fwNfjHOONgilueJDdsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c25e0a908b7aac489975e252beed33c8ccc82dbe485e54c8770dcc93b405493a","last_reissued_at":"2026-05-18T01:01:36.348282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:36.348282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stabilizer Rigidity in Irreducible Group Actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Omer Tamuz, Yair Hartman","submitted_at":"2013-07-29T11:05:18Z","abstract_excerpt":"We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader-Shalom and Nevo-Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader-Shalom and Stuck-Zimmer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7539","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.7539","created_at":"2026-05-18T01:01:36.348405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.7539v3","created_at":"2026-05-18T01:01:36.348405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7539","created_at":"2026-05-18T01:01:36.348405+00:00"},{"alias_kind":"pith_short_12","alias_value":"YJPAVEELPKWE","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YJPAVEELPKWERGLV","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YJPAVEEL","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD","json":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD.json","graph_json":"https://pith.science/api/pith-number/YJPAVEELPKWERGLV4JJL53JTZD/graph.json","events_json":"https://pith.science/api/pith-number/YJPAVEELPKWERGLV4JJL53JTZD/events.json","paper":"https://pith.science/paper/YJPAVEEL"},"agent_actions":{"view_html":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD","download_json":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD.json","view_paper":"https://pith.science/paper/YJPAVEEL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.7539&json=true","fetch_graph":"https://pith.science/api/pith-number/YJPAVEELPKWERGLV4JJL53JTZD/graph.json","fetch_events":"https://pith.science/api/pith-number/YJPAVEELPKWERGLV4JJL53JTZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD/action/storage_attestation","attest_author":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD/action/author_attestation","sign_citation":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD/action/citation_signature","submit_replication":"https://pith.science/pith/YJPAVEELPKWERGLV4JJL53JTZD/action/replication_record"}},"created_at":"2026-05-18T01:01:36.348405+00:00","updated_at":"2026-05-18T01:01:36.348405+00:00"}