{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:P4OXTEMMKPGGKOVHTS33G5SJ45","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":"83e42b50e2de93c785187c0e6d04bb1fdc1d2de64896138856b69fdfccc54bd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-11T20:09:54Z","title_canon_sha256":"0457b54e140053c8f1c780af6907a0fed41b418d41d9707835f1424c43177ad1"},"schema_version":"1.0","source":{"id":"1212.2602","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2602","created_at":"2026-05-18T03:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2602v2","created_at":"2026-05-18T03:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2602","created_at":"2026-05-18T03:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"P4OXTEMMKPGG","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P4OXTEMMKPGGKOVH","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P4OXTEMM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:6c8df81c7314428516c5b7bc0f2cd5d46da025ab8da2acdf9564013c55a82fbf","target":"graph","created_at":"2026-05-18T03:38:35Z","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":"For a weakly mixing bounded rank-one construction the disjointness of its powers is proved. For non-rigid constructions we get minimal self-joinings. Examples of non-mixing rank one actions with explicit weak closure are proposed.","authors_text":"V. V. Ryzhikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-11T20:09:54Z","title":"Minimal Self-Joinings, Bounded Constructions, and Weak Closure of Ergodic Actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2602","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:cff34baf429aaae968f56c018de9155281ff8ba9e4438374ff49d9abd4972037","target":"record","created_at":"2026-05-18T03:38:35Z","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":"83e42b50e2de93c785187c0e6d04bb1fdc1d2de64896138856b69fdfccc54bd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-11T20:09:54Z","title_canon_sha256":"0457b54e140053c8f1c780af6907a0fed41b418d41d9707835f1424c43177ad1"},"schema_version":"1.0","source":{"id":"1212.2602","kind":"arxiv","version":2}},"canonical_sha256":"7f1d79918c53cc653aa79cb7b37649e742e31c8bcc4a598d6c882d2aca08858c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f1d79918c53cc653aa79cb7b37649e742e31c8bcc4a598d6c882d2aca08858c","first_computed_at":"2026-05-18T03:38:35.862017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:35.862017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5eGLEp5jkdI7hvKsb99eFK6bhy8hPoYJez00SssmU6/yE0ISftjfiDmQ6D2irtKQB9uZbcnqbJ2mQxfmzkQtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:35.862616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2602","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cff34baf429aaae968f56c018de9155281ff8ba9e4438374ff49d9abd4972037","sha256:6c8df81c7314428516c5b7bc0f2cd5d46da025ab8da2acdf9564013c55a82fbf"],"state_sha256":"c8acb235198136b69583763ddc2ef59402a8d7cbf7c9a7f7586f5c2ea24515be"}