{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NNCUU3QUTWDXSBERIKFBPTIMCE","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":"404b3af7b5bf2f0d0f9a67fee19d6d8e52d65ccb7ef15f1b10bdf0a926afc84d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-29T20:00:23Z","title_canon_sha256":"d7ed503014f326e51c5c5a64648becc68d2fcf2a1514a7dc11f4cfa37094769f"},"schema_version":"1.0","source":{"id":"1108.5737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5737","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5737v1","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5737","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"NNCUU3QUTWDX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NNCUU3QUTWDXSBER","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NNCUU3QU","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:30aad51e136ce95cccff2bb77ca1edf3c262e138cf834c71978cfa528487727d","target":"graph","created_at":"2026-05-18T04:14:36Z","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":"Given a measure preserving transformation $T$ on a Lebesgue $\\sigma$ algebra, a complete $T$ invariant sub $\\sigma$ algebra is said to split if there is another complete $T$ invariant sub $\\sigma$ algebra on which $T$ is Bernoulli which is completely independent of the given sub $\\sigma$ algebra and such that the two sub $\\sigma$ algebras together generate the entire $\\sigma$ algebra. It is easily shown that two splitting sub $\\sigma$ algebras with nothing in common imply $T$ to be K. Here it is shown that $T$ does not have to be Bernoulli by exhibiting two such non-intersecting $\\sigma$ algeb","authors_text":"Steven Kalikow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-29T20:00:23Z","title":"Non-intersecting splitting algebras in a non-Bernoulli transformation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5737","kind":"arxiv","version":1},"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:f12bf3aa8d5a1f9a5bb49eaebaf53f7fea2ec01bb8fc38de40875c3c6f3b827e","target":"record","created_at":"2026-05-18T04:14:36Z","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":"404b3af7b5bf2f0d0f9a67fee19d6d8e52d65ccb7ef15f1b10bdf0a926afc84d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-29T20:00:23Z","title_canon_sha256":"d7ed503014f326e51c5c5a64648becc68d2fcf2a1514a7dc11f4cfa37094769f"},"schema_version":"1.0","source":{"id":"1108.5737","kind":"arxiv","version":1}},"canonical_sha256":"6b454a6e149d87790491428a17cd0c1115ec30b2ad6964bc682fbe191b0c250c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b454a6e149d87790491428a17cd0c1115ec30b2ad6964bc682fbe191b0c250c","first_computed_at":"2026-05-18T04:14:36.793865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:36.793865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UA9c4ZRfQv8mEVV8NSMw3JRZ0KH8S5BNuZpuMbLtVrVHurggLkkcxVA2QTzNCwCseep7Rolje68LZSzPxF6oCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:36.794331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f12bf3aa8d5a1f9a5bb49eaebaf53f7fea2ec01bb8fc38de40875c3c6f3b827e","sha256:30aad51e136ce95cccff2bb77ca1edf3c262e138cf834c71978cfa528487727d"],"state_sha256":"455d56591ec77e51aadb6c849e0a941ebc9fc22458a111d25c855c40370378ac"}