{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:2QTKEQEMCV5JTUIR5RKOTBI4TM","short_pith_number":"pith:2QTKEQEM","schema_version":"1.0","canonical_sha256":"d426a2408c157a99d111ec54e9851c9b39abd136c952f8f423e362820da0650d","source":{"kind":"arxiv","id":"0908.1173","version":2},"attestation_state":"computed","paper":{"title":"Hilbert C*-modules and amenable actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.FA","authors_text":"Piotr W. Nowak, Ronald G. Douglas","submitted_at":"2009-08-08T15:58:24Z","abstract_excerpt":"We study actions of discrete groups on Hilbert $C^*$-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant."},"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":"0908.1173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-08-08T15:58:24Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"e7ce2bbca6e82270ce1061694ef0ed6563ce5ca2337de00c73a8ed9176da2c6c","abstract_canon_sha256":"c70b91fae6b0381591818be888b05fd659bec2d8221713fc270d733543e55db9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:10.802726Z","signature_b64":"6uj3nYvuk2yLqiKqIFwcrQ1z+TvErpMoiiMxyl+ElI4RHJHD8k6cnS7Swh9cnRRWM7Ir4SqMqkluMUieBp7TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d426a2408c157a99d111ec54e9851c9b39abd136c952f8f423e362820da0650d","last_reissued_at":"2026-05-18T04:16:10.802051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:10.802051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert C*-modules and amenable actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.FA","authors_text":"Piotr W. Nowak, Ronald G. Douglas","submitted_at":"2009-08-08T15:58:24Z","abstract_excerpt":"We study actions of discrete groups on Hilbert $C^*$-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1173","kind":"arxiv","version":2},"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":"0908.1173","created_at":"2026-05-18T04:16:10.802154+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.1173v2","created_at":"2026-05-18T04:16:10.802154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1173","created_at":"2026-05-18T04:16:10.802154+00:00"},{"alias_kind":"pith_short_12","alias_value":"2QTKEQEMCV5J","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"2QTKEQEMCV5JTUIR","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"2QTKEQEM","created_at":"2026-05-18T12:25:58.018023+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/2QTKEQEMCV5JTUIR5RKOTBI4TM","json":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM.json","graph_json":"https://pith.science/api/pith-number/2QTKEQEMCV5JTUIR5RKOTBI4TM/graph.json","events_json":"https://pith.science/api/pith-number/2QTKEQEMCV5JTUIR5RKOTBI4TM/events.json","paper":"https://pith.science/paper/2QTKEQEM"},"agent_actions":{"view_html":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM","download_json":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM.json","view_paper":"https://pith.science/paper/2QTKEQEM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.1173&json=true","fetch_graph":"https://pith.science/api/pith-number/2QTKEQEMCV5JTUIR5RKOTBI4TM/graph.json","fetch_events":"https://pith.science/api/pith-number/2QTKEQEMCV5JTUIR5RKOTBI4TM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM/action/storage_attestation","attest_author":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM/action/author_attestation","sign_citation":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM/action/citation_signature","submit_replication":"https://pith.science/pith/2QTKEQEMCV5JTUIR5RKOTBI4TM/action/replication_record"}},"created_at":"2026-05-18T04:16:10.802154+00:00","updated_at":"2026-05-18T04:16:10.802154+00:00"}