{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:F5CQIUORGGHIYQRUAMVFK2FIAC","short_pith_number":"pith:F5CQIUOR","schema_version":"1.0","canonical_sha256":"2f450451d1318e8c4234032a5568a800bd1e991838d71b01c3a6b604b3b95a5e","source":{"kind":"arxiv","id":"1203.1254","version":2},"attestation_state":"computed","paper":{"title":"Type III factors with unique Cartan decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Cyril Houdayer, Stefaan Vaes","submitted_at":"2012-03-06T17:04:16Z","abstract_excerpt":"We prove that for any free ergodic nonsingular nonamenable action \\Gamma\\ \\actson (X,\\mu) of all \\Gamma\\ in a large class of groups including all hyperbolic groups, the associated group measure space factor $L^\\infty(X) \\rtimes \\Gamma$ has L^\\infty(X) as its unique Cartan subalgebra, up to unitary conjugacy. This generalizes the probability measure preserving case that was established in [PV12]. We also prove primeness and indecomposability results for such crossed products, for the corresponding orbit equivalence relations and for arbitrary amalgamated free products $M_1 *_B M_2$ over a subal"},"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":"1203.1254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-03-06T17:04:16Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"67383d92988c2cb480d51d381979cf60d3e3baf545c7b0497380f707b27cad55","abstract_canon_sha256":"65b0b22fcde31967941315179653868a55a269abd6b5d4d674b50b8f381fb8a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:48.624335Z","signature_b64":"S86EKq16zWmpMxqtGXKnV2fh0eQNPIik1fa6WFCeien3HkfUTwXv773i7TyXxbF7hvNVDzLqKQOzzSR4tjx7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f450451d1318e8c4234032a5568a800bd1e991838d71b01c3a6b604b3b95a5e","last_reissued_at":"2026-05-18T03:12:48.623626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:48.623626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Type III factors with unique Cartan decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Cyril Houdayer, Stefaan Vaes","submitted_at":"2012-03-06T17:04:16Z","abstract_excerpt":"We prove that for any free ergodic nonsingular nonamenable action \\Gamma\\ \\actson (X,\\mu) of all \\Gamma\\ in a large class of groups including all hyperbolic groups, the associated group measure space factor $L^\\infty(X) \\rtimes \\Gamma$ has L^\\infty(X) as its unique Cartan subalgebra, up to unitary conjugacy. This generalizes the probability measure preserving case that was established in [PV12]. We also prove primeness and indecomposability results for such crossed products, for the corresponding orbit equivalence relations and for arbitrary amalgamated free products $M_1 *_B M_2$ over a subal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1254","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":"1203.1254","created_at":"2026-05-18T03:12:48.623743+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1254v2","created_at":"2026-05-18T03:12:48.623743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1254","created_at":"2026-05-18T03:12:48.623743+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5CQIUORGGHI","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5CQIUORGGHIYQRU","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5CQIUOR","created_at":"2026-05-18T12:27:04.183437+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/F5CQIUORGGHIYQRUAMVFK2FIAC","json":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC.json","graph_json":"https://pith.science/api/pith-number/F5CQIUORGGHIYQRUAMVFK2FIAC/graph.json","events_json":"https://pith.science/api/pith-number/F5CQIUORGGHIYQRUAMVFK2FIAC/events.json","paper":"https://pith.science/paper/F5CQIUOR"},"agent_actions":{"view_html":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC","download_json":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC.json","view_paper":"https://pith.science/paper/F5CQIUOR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1254&json=true","fetch_graph":"https://pith.science/api/pith-number/F5CQIUORGGHIYQRUAMVFK2FIAC/graph.json","fetch_events":"https://pith.science/api/pith-number/F5CQIUORGGHIYQRUAMVFK2FIAC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC/action/storage_attestation","attest_author":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC/action/author_attestation","sign_citation":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC/action/citation_signature","submit_replication":"https://pith.science/pith/F5CQIUORGGHIYQRUAMVFK2FIAC/action/replication_record"}},"created_at":"2026-05-18T03:12:48.623743+00:00","updated_at":"2026-05-18T03:12:48.623743+00:00"}