{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HRHD3CBW75RS376VDOFJ2TE2WZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f86c231c4167d4c7cb922083a3113249f72fc8b684c43ec8a3d7464d8842fbf3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-10T09:35:59Z","title_canon_sha256":"fa4c35d9530c2ca488c154dfdfcecee854ad1a44128112a68f6c7f70488613e0"},"schema_version":"1.0","source":{"id":"1201.1995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1995","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1995v2","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1995","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"HRHD3CBW75RS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HRHD3CBW75RS376V","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HRHD3CBW","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:e2d04f79a1f5724b55d28d9bd2304b8024846124fe6e2ec7e8305882422679e8","target":"graph","created_at":"2026-05-18T04:03:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate Gaussian actions through the study of their crossed-product von Neumann algebra. The motivational result is Chifan and Ioana's ergodic decomposition theorem for Bernoulli actions (Ergodic subequivalence relations induced by a Bernoulli action, {\\it Geometric and Functional Analysis}{\\bf 20} (2010), 53-67) that we generalize to Gaussian actions. We also give general structural results that allow us to get a more accurate result at the level of von Neumann algebras. More precisely, for a large class of Gaussian actions $\\Gamma \\curvearrowright X$, we show that any subfactor $N$ of","authors_text":"R\\'emi Boutonnet","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-10T09:35:59Z","title":"On solid ergodicity for Gaussian actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1995","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c947e54c0c062f19cfeab752db67bdf64150bb9978a165032b251ca21d94cd45","target":"record","created_at":"2026-05-18T04:03:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f86c231c4167d4c7cb922083a3113249f72fc8b684c43ec8a3d7464d8842fbf3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-10T09:35:59Z","title_canon_sha256":"fa4c35d9530c2ca488c154dfdfcecee854ad1a44128112a68f6c7f70488613e0"},"schema_version":"1.0","source":{"id":"1201.1995","kind":"arxiv","version":2}},"canonical_sha256":"3c4e3d8836ff632dffd51b8a9d4c9ab652d85735510e8a3cc377e64e2ad768c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c4e3d8836ff632dffd51b8a9d4c9ab652d85735510e8a3cc377e64e2ad768c4","first_computed_at":"2026-05-18T04:03:18.927905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:18.927905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NmCi7cAuE+l+2OXuHBDw/eOkmPN0Sva7WuDrsvcSDq8YyqSee8YIfahuUCnLWCR+g0s25WRXDI3cdYLlMd/dAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:18.928544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c947e54c0c062f19cfeab752db67bdf64150bb9978a165032b251ca21d94cd45","sha256:e2d04f79a1f5724b55d28d9bd2304b8024846124fe6e2ec7e8305882422679e8"],"state_sha256":"29371dd7e52dadab27440edaf247b3dba7ee06ef63effcb9da989b541d9d3142"}