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We show that if $L$ is ergodic on~$X$, and the restriction of~$\\alpha$ to~$X \\times L$ is cohomologous to a homomorphism (modulo a compact group), then, after passing to a finite cover of~$X$, the cocycle $\\alpha$ itself is cohomologous to a homomorphism (modulo a compact group)."},"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":"math/9607219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"1996-07-01T00:00:00Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"39fe2a67ead02adef921f95d5d5a1e819013abb34d07140c64d494534eca7b6c","abstract_canon_sha256":"bbef0ccd1da5b38c7731e3f5d7e7ba0b2299092cd2df095c459c94983c908250"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:47.180818Z","signature_b64":"upOjMxdCRIGQcpeMJoyMKZoi2sWAI+KGrla0CwX7Jcw4LEkASCEndX2PP7vShJcgIEeBLpDA99LN3r+SVa/WBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5160c9a791cff4a07050a686f30861d92cb278551fddc89d0be061c63345a601","last_reissued_at":"2026-05-18T01:05:47.180367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:47.180367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cocycle superrigidity for ergodic actions of non-semisimple Lie groups","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.RT","authors_text":"Dave Witte","submitted_at":"1996-07-01T00:00:00Z","abstract_excerpt":"Suppose $L$ is a semisimple Levi subgroup of a connected Lie group~$G$, $X$ is a Borel $G$-space with finite invariant measure, and $\\alpha \\colon X \\times G \\to \\GL_n(\\real)$ is a Borel cocycle. Assume $L$ has finite center, and that the real rank of every simple factor of~$L$ is at least two. We show that if $L$ is ergodic on~$X$, and the restriction of~$\\alpha$ to~$X \\times L$ is cohomologous to a homomorphism (modulo a compact group), then, after passing to a finite cover of~$X$, the cocycle $\\alpha$ itself is cohomologous to a homomorphism (modulo a compact group)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9607219","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":"math/9607219","created_at":"2026-05-18T01:05:47.180430+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9607219v1","created_at":"2026-05-18T01:05:47.180430+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9607219","created_at":"2026-05-18T01:05:47.180430+00:00"},{"alias_kind":"pith_short_12","alias_value":"KFQMTJ4RZ72K","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"KFQMTJ4RZ72KA4CQ","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"KFQMTJ4R","created_at":"2026-05-18T12:25:48.327863+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/KFQMTJ4RZ72KA4CQU2DPGCDB3E","json":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E.json","graph_json":"https://pith.science/api/pith-number/KFQMTJ4RZ72KA4CQU2DPGCDB3E/graph.json","events_json":"https://pith.science/api/pith-number/KFQMTJ4RZ72KA4CQU2DPGCDB3E/events.json","paper":"https://pith.science/paper/KFQMTJ4R"},"agent_actions":{"view_html":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E","download_json":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E.json","view_paper":"https://pith.science/paper/KFQMTJ4R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9607219&json=true","fetch_graph":"https://pith.science/api/pith-number/KFQMTJ4RZ72KA4CQU2DPGCDB3E/graph.json","fetch_events":"https://pith.science/api/pith-number/KFQMTJ4RZ72KA4CQU2DPGCDB3E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E/action/storage_attestation","attest_author":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E/action/author_attestation","sign_citation":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E/action/citation_signature","submit_replication":"https://pith.science/pith/KFQMTJ4RZ72KA4CQU2DPGCDB3E/action/replication_record"}},"created_at":"2026-05-18T01:05:47.180430+00:00","updated_at":"2026-05-18T01:05:47.180430+00:00"}