{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3FX2JBKDSZUGNEOZS2XL55PJTD","short_pith_number":"pith:3FX2JBKD","schema_version":"1.0","canonical_sha256":"d96fa4854396686691d996aebef5e998e9cc6ca7d8f37ac314498e2ba6e1323a","source":{"kind":"arxiv","id":"1404.0246","version":1},"attestation_state":"computed","paper":{"title":"The Morse minimal system is nearly continuously Kakutani equivalent to the binary odometer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Dykstra, Ayse Sahin","submitted_at":"2014-04-01T14:17:06Z","abstract_excerpt":"Ergodic homeomorphisms $T$ and $S$ of Polish probability spaces $X$ and $Y$ are evenly Kakutani equivalent if there is an orbit equivalence $\\phi: X_0 \\rightarrow Y_0$ between full measure subsets of $X$ and $Y$ such that, for some $A \\subset X_0$ of positive measure, $\\phi$ restricts to a measurable isomorphism of the induced systems $T_A$ and $S_{\\phi(A)}$. The study of even Kakutani equivalence dates back to the seventies, and it is well known that any two zero-entropy loosely Bernoulli systems are evenly Kakutani equivalent. But even Kakutani equivalence is a purely measurable relation, wh"},"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":"1404.0246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-01T14:17:06Z","cross_cats_sorted":[],"title_canon_sha256":"6ba4c071b18c7bcbd13aa8e670e951c40dcb061965126ad9b5c5830c75e5ca8c","abstract_canon_sha256":"956e51f0de0469f94267bf379219410c4ddfd769022401c4a31b25d41de51823"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:04.810796Z","signature_b64":"tBxOCeTQTlE4uSEjE2YIz05kL+Isklm6vHmWkXAAsafyPmS0ybJfTlN4b2NHgJc9VUn0yR/JEKw9arAVSboFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d96fa4854396686691d996aebef5e998e9cc6ca7d8f37ac314498e2ba6e1323a","last_reissued_at":"2026-05-18T02:55:04.810399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:04.810399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Morse minimal system is nearly continuously Kakutani equivalent to the binary odometer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Dykstra, Ayse Sahin","submitted_at":"2014-04-01T14:17:06Z","abstract_excerpt":"Ergodic homeomorphisms $T$ and $S$ of Polish probability spaces $X$ and $Y$ are evenly Kakutani equivalent if there is an orbit equivalence $\\phi: X_0 \\rightarrow Y_0$ between full measure subsets of $X$ and $Y$ such that, for some $A \\subset X_0$ of positive measure, $\\phi$ restricts to a measurable isomorphism of the induced systems $T_A$ and $S_{\\phi(A)}$. The study of even Kakutani equivalence dates back to the seventies, and it is well known that any two zero-entropy loosely Bernoulli systems are evenly Kakutani equivalent. But even Kakutani equivalence is a purely measurable relation, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0246","kind":"arxiv","version":1},"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":"1404.0246","created_at":"2026-05-18T02:55:04.810456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.0246v1","created_at":"2026-05-18T02:55:04.810456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0246","created_at":"2026-05-18T02:55:04.810456+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FX2JBKDSZUG","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FX2JBKDSZUGNEOZ","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FX2JBKD","created_at":"2026-05-18T12:28:11.866339+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/3FX2JBKDSZUGNEOZS2XL55PJTD","json":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD.json","graph_json":"https://pith.science/api/pith-number/3FX2JBKDSZUGNEOZS2XL55PJTD/graph.json","events_json":"https://pith.science/api/pith-number/3FX2JBKDSZUGNEOZS2XL55PJTD/events.json","paper":"https://pith.science/paper/3FX2JBKD"},"agent_actions":{"view_html":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD","download_json":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD.json","view_paper":"https://pith.science/paper/3FX2JBKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.0246&json=true","fetch_graph":"https://pith.science/api/pith-number/3FX2JBKDSZUGNEOZS2XL55PJTD/graph.json","fetch_events":"https://pith.science/api/pith-number/3FX2JBKDSZUGNEOZS2XL55PJTD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD/action/storage_attestation","attest_author":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD/action/author_attestation","sign_citation":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD/action/citation_signature","submit_replication":"https://pith.science/pith/3FX2JBKDSZUGNEOZS2XL55PJTD/action/replication_record"}},"created_at":"2026-05-18T02:55:04.810456+00:00","updated_at":"2026-05-18T02:55:04.810456+00:00"}