{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MTWXYHSFD4GKC6AJA2K35ZG4M3","short_pith_number":"pith:MTWXYHSF","schema_version":"1.0","canonical_sha256":"64ed7c1e451f0ca178090695bee4dc66eef6e00bd30cf74d251939cfc6cf8cfa","source":{"kind":"arxiv","id":"1201.5367","version":1},"attestation_state":"computed","paper":{"title":"Rigidity of group actions on homogeneous spaces, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Furman, Alex Gorodnik, Barak Weiss, Uri Bader","submitted_at":"2012-01-25T20:46:24Z","abstract_excerpt":"Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice {\\Gamma} acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors and joinings defined apriori only in the measurable category are in fact algebraically constrained. Arguing in an elementary fashion we manage to classify all the measurable {\\Phi} commuting with the {\\Gamma}-action: assuming ergodicity, we find they are algebraically defined."},"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":"1201.5367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-25T20:46:24Z","cross_cats_sorted":[],"title_canon_sha256":"f499e644034682263cecbb7324e33968656bef1aea9e2607a98861971a9d356e","abstract_canon_sha256":"68933cc0f2d0762048d765d8232d546ce5273706832407ceab07d267fa5409ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:21.832181Z","signature_b64":"N0TrZl6mteVd/revB0Rk+h+uY9INLJhdrI/Mxao8bwNyx9yiOIWfTi2OzmxTuLWkN+KXN8sDTd/jPo1CZAVSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64ed7c1e451f0ca178090695bee4dc66eef6e00bd30cf74d251939cfc6cf8cfa","last_reissued_at":"2026-05-18T01:28:21.831559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:21.831559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of group actions on homogeneous spaces, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Furman, Alex Gorodnik, Barak Weiss, Uri Bader","submitted_at":"2012-01-25T20:46:24Z","abstract_excerpt":"Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice {\\Gamma} acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors and joinings defined apriori only in the measurable category are in fact algebraically constrained. Arguing in an elementary fashion we manage to classify all the measurable {\\Phi} commuting with the {\\Gamma}-action: assuming ergodicity, we find they are algebraically defined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5367","kind":"arxiv","version":1},"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":"1201.5367","created_at":"2026-05-18T01:28:21.831641+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5367v1","created_at":"2026-05-18T01:28:21.831641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5367","created_at":"2026-05-18T01:28:21.831641+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTWXYHSFD4GK","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTWXYHSFD4GKC6AJ","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTWXYHSF","created_at":"2026-05-18T12:27:14.488303+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/MTWXYHSFD4GKC6AJA2K35ZG4M3","json":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3.json","graph_json":"https://pith.science/api/pith-number/MTWXYHSFD4GKC6AJA2K35ZG4M3/graph.json","events_json":"https://pith.science/api/pith-number/MTWXYHSFD4GKC6AJA2K35ZG4M3/events.json","paper":"https://pith.science/paper/MTWXYHSF"},"agent_actions":{"view_html":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3","download_json":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3.json","view_paper":"https://pith.science/paper/MTWXYHSF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5367&json=true","fetch_graph":"https://pith.science/api/pith-number/MTWXYHSFD4GKC6AJA2K35ZG4M3/graph.json","fetch_events":"https://pith.science/api/pith-number/MTWXYHSFD4GKC6AJA2K35ZG4M3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3/action/storage_attestation","attest_author":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3/action/author_attestation","sign_citation":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3/action/citation_signature","submit_replication":"https://pith.science/pith/MTWXYHSFD4GKC6AJA2K35ZG4M3/action/replication_record"}},"created_at":"2026-05-18T01:28:21.831641+00:00","updated_at":"2026-05-18T01:28:21.831641+00:00"}